The outdoor stage was all set in Wilmington, Del., for Joseph R. Biden Jr. to come out and address the nation — presumably in a victory speech as the president-elect.
There were banners and spotlights and people in cars ready to honk their approval for the next president and his running mate, Senator Kamala Harris. But the hour grew late and the counting of votes kept going, and going with no sign of a winner in the contest between Mr. Biden and President Trump.
Finally, close to 11 p.m., Mr. Biden emerged. He did not deliver a victory speech, but came as close as he could, talking about what he intended to do as president while assuring Americans “your vote will be counted.” It was clear that Mr. Biden was getting as restless with the long, laborious count as much of the country.
“It’s as slow as it goes,” Mr. Biden said, describing watching the numbers dribble in on television. “As slow as it goes it can be numbing.”
It has now been four days since Election Day. As long as that might seem, it’s nowhere near the 36 days it took in 2000 before the Supreme Court ended the counting and effectively declared George W. Bush the winner over Al Gore.
While all indications suggest that Mr. Biden has succeeded in defeating Mr. Trump, it’s still close enough in four states — Arizona, Nevada, Pennsylvania and Georgia — that the contest remains unresolved.
As the number of outstanding ballots slowly dwindled, Mr. Trump was left increasingly with only legal challenges to forestall defeat. He remained uncharacteristically out of sight on Friday.
This postelection limbo was one more bit of evidence of what a strange election this has been. Ballot counters have been overwhelmed by the record number of early votes cast by mail because of the pandemic; hence the slow, meticulous counts taking place across the country.
Most elections come to an end when one candidate calls the other to concede. Mr. Trump may be trailing — with diminishing hopes of winning — but he’s not the kind of person who concedes. And it’s not in Mr. Biden’s political interest to unilaterally declare victory (as Mr. Trump has effectively done), and feed the conspiracy theory being pushed by the president and his supporters that Democrats are trying to steal the election.
So the count goes on. And on. And on.
PHILADELPHIA — As Joseph R. Biden Jr. increased his lead over President Trump in Pennsylvania, Democrats grew increasingly confident that he would win the state and with it the presidency: The state’s 20 electoral votes would put Mr. Biden, who has 253 electoral votes, past the 270-vote threshold for victory.
Mr. Biden had steadily erased Mr. Trump’s early lead in the state — at one point, the president led by half a million votes — as ballots, mostly absentee and mail-in votes, were counted over the past few days. Most of the remaining uncounted votes in the state are in Democratic-leaning areas.
The Biden campaign hoped further counting could push their lead above 0.5 percent, obviating the need for a recount there and potentially setting the stage for television networks to declare Mr. Biden the winner.
In Allegheny County, a predominantly Democratic area that includes Pittsburgh, election workers were going through roughly 20,000 mail-in ballots and additional provisional ballots on Saturday, Rich Fitzgerald, the county executive, said in a televised interview.
The county’s mail-in ballots have so far been won overwhelmingly by Mr. Biden, as have the provisional ballots. Mr. Fitzgerald said the county could begin reporting votes by late morning or early afternoon.
With 96 percent of votes reported by 7:30 a.m., Mr. Biden led in Pennsylvania by nearly 29,000 votes, precariously close to the critical margin of 0.5 percent, which triggers a recount.
Mr. Fitzgerald cautioned that the last ballots to count will be the trickiest, requiring additional checks to ensure they were not duplicates, which could slow the process.
Responding to baseless allegations by the Trump campaign of vote-counting secrecy, he said that observers and journalists had access to the vote-counting site and that there were as many surveillance cameras there as in a casino.
Nearly a dozen lawsuits filed by President Trump and his allies are working their way through the courts in Nevada, Pennsylvania, Michigan and Georgia, trying — so far unsuccessfully — to stop ballot counting and invalidate enough votes to erase Joseph R. Biden Jr.’s leads there. Here is a look at those cases.
In Pennsylvania, the biggest fight has been over ballots that were postmarked by Election Day but arrive later. In September, the state Supreme Court ruled, over Republican objections, that election officials could accept ballots arriving up to three days later. The U.S. Supreme Court declined to intercede, but left open the possibility that it could revisit the question.
Separately, the Supreme Court did grant the Trump camp a minor victory in Pennsylvania on Friday evening, when Justice Samuel A. Alito Jr. ordered election officials there to keep the late-arriving ballots separate from other ballots, and not to include them, for now, in announced vote totals. But the victory was essentially in name only: Pennsylvania’s secretary of state had already given that instruction.
The entire dispute over the late-arriving ballots could be moot, because Mr. Biden has taken the lead in Pennsylvania even without them.
One of several other Pennsylvania disputes involves people from both parties who observe the tabulation in Philadelphia, where they were told to stay 10 feet away from the vote counters. Some Trump allies have claimed, falsely, that no observers were allowed. In response to a Republican complaint, a judge ruled on Thursday that they could stand within six feet, but refused to stop the counting.
A similar case in Michigan was thrown out.
In Nevada, the Trump campaign has sued to stop the processing of mail ballots, claiming that its monitors had inadequate access. A judge denied the request, citing a lack of evidence. Another Republican suit claimed lax authentication of ballots; a judge dismissed it.
An Arizona lawsuit claims that ballots filled out with felt-tipped pens were being discarded; state and federal officials say that is false. A case in Georgia claims that a few dozen late-arriving ballots — which the state does not allow, even if they are postmarked by Election Day — were not properly set apart, raising the possibility that they would be counted. A judge threw out the complaint, saying there was no evidence that the ballots in question had arrived late.
As the country waits for ballot tallies in a handful of crucial battleground states, the Trump campaign has pursued lawsuits in Michigan and Pennsylvania, and said that it would demand a recount in Wisconsin.
If lawsuits and recounts persist — and if vote margins are razor thin in key swing states — it could be weeks before President Trump or Joseph R. Biden Jr. is named the winner. In some scenarios, the contest could drag into 2021, and might look something like this:
Even before Election Day, armies of lawyers for the Trump and Biden campaigns were preparing for an onslaught of litigation. Mr. Trump has long pushed allegations of voter fraud without evidence and raised questions about the validity of the mail-in vote.
“This election won’t be resolved until a losing candidate concedes defeat and congratulates his opponent,” said Edward B. Foley, an Ohio State University law professor. “And if the candidates don’t give us finality that way, then the legal process has to give it to us.”
Senator David Perdue, Republican of Georgia, was fighting for his political life on Saturday in a contest that could determine which party controls the Senate, as his re-election bid headed to a January runoff against Jon Ossoff, his Democratic challenger.
Mr. Perdue had a razor-thin lead over Mr. Ossoff in a contest that demonstrated Democrats’ emerging strength in what was once a Republican stronghold in the Deep South. Neither candidate claimed a majority of votes amid a protracted count, according to The Associated Press.
The inconclusive result set up a dramatic rematch between Mr. Perdue and Mr. Ossoff on Jan. 5, and thrust Georgia into the center of the nation’s political fray as Joseph R. Biden Jr. appeared on track to win the White House. The state had already been slated to decide the fate of its other Senate seat in a special-election runoff between the Rev. Dr. Raphael Warnock, a Democrat, and Senator Kelly Loeffler, a Republican, the same day. That makes it nearly certain that the twin Georgia races will determine which party controls the chamber just two weeks before the next presidential inauguration.
“Change has come to Georgia,” Mr. Ossoff said at a rally on Friday, “and Georgia is a part of the change coming to America.”
If Mr. Biden wins the White House, and Democrats take both of Georgia’s seats, they would draw the Senate to a 50-50 tie, effectively taking control of the chamber, given the vice president’s power to cast tiebreaking votes. But that is a tall order in a state with deep conservative roots, and Republicans felt reasonably confident they could hang onto at least one of the seats needed to deny Democrats the majority.
Two other Senate races, in North Carolina and in Alaska, had not yet been called. But Republicans were leading in both and expected to win, putting them at 50 seats to the Democrats’ 48.
ATLANTA — As former Vice President Joseph R. Biden Jr. took a narrow lead over President Trump in Georgia, Georgia’s secretary of state said Friday that the presidential race there was so close that a recount was inevitable.
By early Saturday morning, Mr. Biden led Mr. Trump in Georgia by about more than 7,000 votes.
“With a margin that small, there will be a recount in Georgia,” the secretary of state, Brad Raffensperger, said Friday morning at the state Capitol.
He added: “The final tally in Georgia at this point has huge implications for the entire country. The stakes are high and emotions are high on all sides. We will not let those debates distract us from our work. We will get it right, and we will defend the integrity of our elections.”
Gabriel Sterling, an official with the secretary of state’s office, said that a pool of about 4,200 ballots — most of them absentee ballots — remained to be tallied in four counties: Gwinnett, Cobb, Cherokee and Floyd. The largest tranche to be counted was in Gwinnett County, which contains Atlanta suburban communities and has gone from leaning Republican to leaning Democratic in recent years.
The state must also deal with ballots from military and overseas voters, which will be counted if they arrive in the mail before the end of business Friday and were postmarked by Tuesday.
Mr. Sterling said that the unofficial tally of the votes could be completed by the end of the weekend.
Flipping Georgia, a state last won by a Democrat in 1992, and where Mr. Trump won by more than 200,000 votes four years ago, would represent a significant political shift this year, but the state has shown signs of trending blue. When Mr. Trump defeated Hillary Clinton in 2016, he did so by five percentage points, a far slimmer margin than Republicans had enjoyed in previous presidential elections.
Mr. Biden’s late surge in this year’s count, thanks to his dominance in Atlanta, Savannah and the increasingly Democratic-friendly suburbs around both, transformed the competition in a traditionally Republican-leaning state into one of the closest contests in the nation.
As the count narrowed and it appeared that the two candidates would be separated by the slimmest of margins, Democrats urged voters in the state to fix ballots that had been rejected because of invalid or missing signatures before the deadline on Friday evening.
Those who voted absentee — a group that this year has been heavily Democratic — could check online to see whether election officials had accepted or rejected their ballots. Absentee ballots are often rejected when the voter forgets to sign or uses a signature that does not match the one on file with the state, in some cases because the filed signature is many years old. Election officials are supposed to contact voters in such cases but are not always able to do so.
Voters had until 5 p.m. on Friday to submit an affidavit form to “cure” such ballots. With Georgia hanging in the balance as the last votes were counted, national Democrats — including Representative Alexandria Ocasio-Cortez of New York — were amplifying the message in hopes of salvaging every vote possible.
Perhaps no one wants the election to end more than the vote counters themselves.
With tens of thousands of ballots still to be counted in states where President Trump and Joseph R. Biden were separated by slim margins — and an anxious nation riveted by every change in the count — a small army of workers continued to tally votes four days after the polls closed.
Beyond the tedium and the exhaustion, they were facing the added stress of trying to keep themselves safe as coronavirus cases in the United States hit record highs. Still, with masks covering their faces and gloves guarding their hands, they soldiered on into Saturday and stood ready to continue at their task into next week.
In some election offices, safety measures including social distancing, meant that fewer ballot counters could work at the same time than in previous elections, slowing the process.
At least one election official in the Westmoreland County, Pa., tested positive for the coronavirus this week, according to the news website Lancaster Online.
And, while many polling stations use scanners to process ballots thousands of ballots rapidly, at this point in the count they were also processing ballots that could not be read by machines for a variety of reasons.
Some of the most challenging ballots to count are faulty ones. Alleghany County in Pennsylvania is still processing nearly 30,000 ballots affected by a printing error. Provisional ballots also take time to process, since they are generally reviewed individually by the county boards of election or local election officials.
While each state has its own rules and methods, the scene in West Chester, Pa., was a familiar one. Election workers, seated under fluorescent lights, sorting and feeding ballots by hand into high-speed scanners. At this station, weary workers were given the weekend off and will resume counting inside the university gym Monday morning.
But others worked through the night and into the morning on Saturday. While they counted, independent observers watched over their shoulders and some places offered livestreaming feeds online for members of the public to watch scenes like the one at the Pennsylvania Convention Center in Philadelphia. It was not exactly packed with action, but more like suspended animation as workers in neon yellow and orange jackets sat opposite ends of tables methodically tabulating ballots.
The process could be tedious but no detail was too small for a citizenry hungry for information. Local media in Pennsylvania was filled on Saturday morning with descriptions of how ballot counters would load envelopes into machines twice: first to slice them open and then a second time to open the smaller, inner “secrecy” envelopes. Ballot counters then unfold the ballots by hand and feed them into high-speed scanners. From there, the results are saved onto memory sticks, WHYY-FM, a public radio station in Philadelphia, told its listeners.
Evelyn Smith, a graduate student in economics at the University of Michigan who counted ballots for 13 hours on Election Day, said she found the monotony of the process tedious, but meditative.
For a salary of $13 an hour, she worked from a high-school cafeteria in Ann Arbor, Mich., sorting ballots and delivering them to the next station. She said election officials at her center wore masks, but it was not always possible to maintain social distancing.
“It’s a risky thing to do, but it’s essential work,” she said.
Phil Armstrong, the county executive in Lehigh County, Pa., said it was impossible to respect social-distancing rules at the vote-counting center, given all of the ballot counters, lawyers and election observers from both parties who were present.
“It was pretty crowded,” he said. Still, the vibe was upbeat, and different tables of ballot counters had friendly competitions about how many ballots they had counted in a certain period of time.
On Friday, after a very long week, he sent counters home for a break over the weekend.
“I said, ‘We’re not running a sweatshop here,’” he said. “That upsets both parties, but you know, I’m sorry, I have to do what’s best for my people.”
Joseph R. Biden Jr. widened his lead over President Trump in Nevada by early Saturday morning from about 11,000 votes to about 22,650, and moved closer to victory there, as his advantage over Mr. Trump grew to 1.8 percentage points.
Nevada has six electoral votes and its entire Election Day vote has been counted; the late mail and provisional ballots that remain lean Democratic. About 9 percent of the state’s votes have yet to be tabulated.
Final results might not be announced until Saturday or Sunday, elections officials have said.
The Trump campaign has already identified Nevada, which allows any losing candidate to request a recount, as one of the battleground states where it hopes to use the courts and procedural maneuvers to stave off defeat in the Electoral College. Less than 24 hours before Election Day, a Nevada judge rejected a lawsuit filed by Republicans who had tried to stop early vote counting in Clark County.
Since Mrs. Clinton beat Mr. Trump in Nevada by 2.4 percentage points in 2016, the state has turned a deeper shade of blue, with Democrats controlling the governor’s office and legislature, both Senate seats and all but one House seat. It was not widely expected to be a battleground state this year.
But while recent polls consistently showed Mr. Biden ahead of Mr. Trump in Nevada, Democrats worried that the pandemic would make it difficult to create a robust election turnout operation. The state has reported more than 104,000 coronavirus cases.
PHOENIX — Former Vice President Joseph R. Biden Jr. has maintained a steady but narrowing lead in Arizona vote tallies after Election Day, with Latino voters lining up behind the former vice president in a state that President Trump won by three and a half percentage points in 2016.
By early Saturday morning, Mr. Biden’s advantage stood at just under 30,000 votes.
Even Mr. Biden’s narrow edge underscored a profound political shift in Arizona, a longtime Republican bastion that has lurched left in recent years, fueled by rapidly evolving demographics and a growing contingent of young Latino voters who favor liberal policies.
In one of the brightest spots for Democrats so far, the former astronaut Mark Kelly defeated the state’s Republican senator, Martha McSally, in a special election, making Mr. Kelly and Kyrsten Sinema the first pair of Democrats to represent Arizona in the Senate since the 1950s.
Stacey Abrams, who earlier this year was on a short list of potential vice-presidential candidates, was ultimately not chosen by Joseph R. Biden Jr. But on Friday, as Mr. Biden took a narrow lead in Georgia, it was Ms. Abrams who was celebrated, a sign of her remarkable ascent as a power broker since her failed bid for governor of that state two years ago.
Celebrities, activists and voters across Georgia credited Ms. Abrams with moving past her loss — she came within 55,000 votes of the governor’s mansion — and building a well-funded network of organizations that highlighted voter suppression in the state and inspired an estimated 800,000 residents to register to vote.
“You have to build the infrastructure to organize and motivate your base, and you have to persuade people,” said Jason Carter, a Democrat who was the party’s candidate for governor in 2014. “Stacey built that infrastructure, and Donald Trump’s presidency energized that infrastructure, and it opened up voters to persuasion who were previously not open, particularly in the suburbs.”
Mr. Biden pulled ahead of President Trump in Georgia, a state that has not elected a Democratic presidential candidate in nearly three decades, and maintained a slight lead throughout Friday. He was up about 4,100 votes Friday evening with more than 98 percent of the ballots counted. Because of the small margin, the secretary of state confirmed there would be a recount.
Still, Democrats in the state were jubilant.
Ms. Abrams declined to comment on Friday. But in a tweet, she wrote, “My heart is full.” And she cited the work of other activists. “Georgia, let’s shout out those who’ve been in the trenches and deserve the plaudits for change.”
If Mr. Biden holds onto his slim lead in Georgia, her profile is likely to grow.