Mr. Kennedy sees himself as the leader of a populist movement that has tapped into a vein of anti-establishment outrage and government skepticism. He knows that some of his most die-hard fans — the ones Mr. Trump was eager to bring into his fold — want to see Mr. Kennedy hold real power.

Whether it is ego or political strategy aimed at drawing votes to Mr. Trump (or both), Mr. Kennedy continues to center himself in his pitch.

In a message that Mr. Kennedy has posted several times on social media since he bowed out of the race in August, he has urged his followers not to vote for him, even though he may still be on the ballot in their state. “No matter what state you live in, you should be voting for Donald Trump,” he said. “That’s the only way we can get me and everything I stand for into Washington, D.C., and fulfill the mission that motivated my campaign.”

In another message, Mr. Kennedy says: “If Donald Trump wins re-election with a strong mandate, then no one will be able to stop us. When he empowers me to clean up corruption and the federal agencies, and especially our health agencies, you know what’s at stake here.”

Mr. Kennedy’s focus on his own plans is apparent in his repeated insistence that he has been promised a significant role in a potential second Trump administration — at times getting out ahead of Trump campaign and transition officials. “I want to be in the White House, and he has assured me that I’m going to have that,” Mr. Kennedy said of Mr. Trump in a Fox News appearance on Sunday.

In September, The New York Times reported, based on people who were briefed on private conversations, that in the weeks leading up to Mr. Kennedy’s suspending his campaign, many people in his orbit were skeptical of a potential alliance with Mr. Trump. The former president, they felt, had a track record of breaking promises.

But Mr. Kennedy felt that aligning with Mr. Trump would give him more power to address the issues he had described throughout his campaign: chronic disease, censorship, corporate power in government, the war in Ukraine.

Mr. Trump has not wholly subsumed Mr. Kennedy’s world. Perhaps the best evidence of this is the branding of the “Make America Healthy Again” movement, a take on “Make America Great Again” that took off in the days after Mr. Kennedy’s endorsement and that has become a kind of offshoot of the Trump campaign.

MAHAnow.org is the evolution of the Kennedy campaign’s website. There, supporters can contribute $47 to be featured on a mosaic depicting Mr. Kennedy and Mr. Trump shaking hands. The image, Mr. Kennedy wrote on X, commemorates “the historic moment when I endorsed Donald Trump.”

The former president kicked off Monday, the final day before Election Day, at the Dorton Arena in Raleigh, N.C., where the section behind the stage still had several dozen empty seats when he finally took the stage about an hour later than expected. There were a couple thousand supporters inside, but the back of the arena had several empty rows. And there was no line outside.

During the final week of his campaign, Mr. Trump has at times been delivering boasts about crowd size in arenas that are far from packed to the rafters. And when he insists that thousands more are waiting outside, they are often not.

On Saturday, his campaign curtained off the upper bowl of an arena in Greensboro, N.C., that Vice President Kamala Harris had filled. Seating in the lower bowl wasn’t packed either. And whole sections of Fiserv Forum, his last stop in Milwaukee, were empty on either side of the stage on Friday.

Crowd sizes are not a perfect sign of political or electoral support, particularly in the final stages of a race in states that Mr. Trump has visited frequently. His Greensboro rally was his second event in the city in two weeks. And North Carolina in particular has had a record early turnout: The state’s Board of Elections announced that nearly 4.5 million voters cast ballots during early in-person voting.

But Mr. Trump often uses his audiences as an indicator of his support, particularly as he reminisces about his 2016 campaign, when he beat Hillary Clinton. And as he tries to defeat Ms. Harris this year, he uses his crowds to back up his insistence that his election is all but assured, making the empty gaps in his venues more notable.

Over the nine years since Mr. Trump rode down a golden escalator toward his political career, his ability to keep audiences captivated throughout increasingly long, winding speeches — and through lengthy delays as he runs behind schedule — has also seemed to weaken.

Ms. Harris, in an attempt to needle Mr. Trump, brought up the exits at their presidential debate in September. “People start leaving his rallies early out of exhaustion and boredom,” she said, an attack that sent him on a tangent that night.

Mr. Trump has at several rallies since then falsely insisted that Ms. Harris was lying and that people would never leave his rallies early, even as some were in the process of doing so.

“We’ve done this for nine years,” Mr. Trump said at a rally last week in Rocky Mount, N.C. “We had the greatest rallies in the history of the world, chancellors and prime ministers. People would tell me they watch the rallies from Europe.” He added: “They try and demean us like that horrible, horrible person that I debated where she said, ‘And people leave early.’ Nobody leaves early.”

On Sunday, he arrived two hours late to a small airport in Kinston, N.C., where hundreds were waiting on the tarmac. But within five minutes of the start of his speech, a stream of audience members began heading for the exit, a steady exodus that never quite abated.

The crowd at his jam-packed Madison Square Garden rally, billed as the signature event of his closing stretch, didn’t stick through his speech.

And at a speech at an arena last month on the Penn State campus in State College, Pa., Mr. Trump opened with several direct promises to boost the fortunes of young voters, before groups of them began leaving minutes later. Mr. Trump took the stage at 5:40 p.m. A Penn State football game was scheduled to kick off less than two hours later.

“I don’t know exactly how to measure it, but it certainly feels like an enormous problem,” said Amy Cohen, the executive director of the National Association of State Election Directors. “It just feels so, so difficult to get our arms around it.”

Here are five reasons this year’s early voting period is flooded with falsehoods.

1. Early voting has increased

More voters have embraced early voting and mail-in voting since 2020, creating a longer period of interaction between voters and election officials. That has inadvertently led to the kind of tense and confusing exchanges that can spin into controversy online and spread wildly before the facts are known.

Pennsylvania officials, for example, have spent the early voting period battling one falsehood after another, including a claim that a postal worker committed voter fraud when a video showed that he was simply delivering mail-in ballots.

“The period of time to generate all of those Election Day rumors is stretched out across all of these early in-person voting periods,” said Kate Starbird, a founder of the Center for an Informed Public at the University of Washington.

2. Foreign agents are pushing fake videos

A viral video posted on Oct. 24 appeared to show election workers tearing up ballots. Another seemed to show illegal immigrants who had successfully registered to vote.

Neither video was authentic. The videos were “manufactured and amplified” by Russian agents, according to statements by the Federal Bureau of Investigation.

The videos underscored the continuing role that Russia and other foreign governments have tried to assert over U.S. elections, amplifying Mr. Trump’s false claims of voter fraud.

“The Russians in particular are using many more platforms, and smaller platforms, to target more precisely their divisive and pro-Trump disinformation,” said Paul Barrett, deputy director of the N.Y.U. Stern Center for Business and Human Rights, who studies online disinformation.

3. Social media is more permissive

Social media companies, especially X, have adopted a more permissive posture around voter fraud claims. Under Elon Musk’s leadership, X unraveled its moderation layers and has allowed far-right conspiracy theorists back on the platform.

Mr. Musk has also become a chief purveyor of misleading claims, amplifying accounts known for sharing conspiracy theories to his 202 million followers and raising questions about the voting process that have put election administrators on the defensive.

“Let’s be clear: @elonmusk is spreading dangerous disinformation,” Jocelyn Benson, Michigan’s Secretary of State, wrote on X this week, after Mr. Musk shared misleading information about the state’s voter rolls.

Mr. Musk did not respond to a request for comment.

A report by Free Press, a nonprofit media watchdog, released on Thursday concluded that the “online landscape is worse in 2024 than in previous election cycles.” It found major platforms like Facebook and YouTube were less committed to policing misinformation and were less responsive to requests from watchdogs.

In separate statements, YouTube and Facebook said they continued to invest in safety and security on their platforms. YouTube said there have been no cuts to its Trust and Safety team. Meta, which owns Facebook, said the number of fact-checking partners increased to more than 100 this year, from 80 during the 2020 election.

4. Trump’s rhetoric is bolder

Former President Donald J. Trump has long pushed false voter fraud theories, but never this much or with this level of fervor, experts said.

His claims have continued on social media during the early voting period, including a falsehood last week on Truth Social that “Pennsylvania is cheating, and getting caught, at large scale levels rarely seen before.”

“It wasn’t part of his standard speech the way it has been lately,” Steven Brill, a co-founder of NewsGuard, said of the change since 2020. “It’s just a world of difference.”

5. Voter fraud claims are now crowdsourced

Mr. Musk’s political group, America PAC, started an “election integrity” channel on X this month where users are encouraged to post and share “potential instances of voter fraud and irregularities.” The portal includes rumors and anecdotes about potential voting issues, including videos of voters using drop boxes alongside baseless claims that they are stuffing them with votes.

The Republican National Committee also unveiled a portal, called Protect the Vote, in April that aimed to get 100,000 volunteers to monitor and submit potential cases of voter fraud.

True the Vote, an organization that has been sued for spreading falsehoods about election integrity, rolled out its own portal this year called Vote Alert. Among dozens of claims listed there is a false report about Dominion Voting Systems, the voting machine company targeted by falsehoods in 2020. The report claimed that a Dominion voting machine displayed both a “public” and “private” vote counter and that those numbers did not match, suggesting possible ballot manipulation. A representative for Dominion said that she was baffled by the claim and that no such counters exist on its machines.

True the Vote did not immediately respond to a request for comment.

The portals are presented as straightforward efforts to collect information about voting issues. But many of the stories described in the posts are unverifiable rumors. In a report, the Center for an Informed Public warned that posts like these could be used to “argue that certain races should not be certified,” among other risks.

“This adds up to a dangerous situation, as the line between fact and anti-democratic falsehood has blurred far more severely than it did during the 2020 election cycle,” said Mr. Barrett of N.Y.U. “I fear we are in for a very rough ride.”

“The next day, my neighbor just ignored me in the grocery store,” said Ms. Ruttum, a now-retired nurse. “I said, ‘Hey, how are you?’ She said to me, ‘I never knew you were one of those.’”

Sixteen years after Ms. Ruttum’s Obama sign caused a stir in Elm Grove, which was once among the most Republican communities in Wisconsin’s most populous and important G.O.P. county, the village is on the verge of backing Vice President Kamala Harris for president.

As places like Elm Grove and its much larger Waukesha County neighbor, Brookfield, gradually shift from Republican dominance to tossup status, they have chipped away at the party’s advantage in right-leaning suburbs across the country. And without running up a big victory of more than 20 percentage points in Waukesha County, the statewide math becomes next to impossible for Republicans, who cannot overcome the Democratic advantages in Madison and Milwaukee through the state’s rural red counties alone.

In so many places in the presidential battleground states, the election has become a game of margins. Nowhere is this clearer than in Elm Grove and Brookfield, where Ms. Harris and former Representative Liz Cheney held an event last month that was an explicit appeal to Republicans skeptical of former President Donald J. Trump. Just a decade ago, these communities made up the beating heart of the state’s Republican base in Waukesha County.

As in so many American suburbs, politics in Elm Grove and Brookfield shifted left when Mr. Trump took over the Republican Party. Mitt Romney took nearly 70 percent of the vote in the two communities 2012, but Mr. Trump won with a little over 50 percent in 2020.

Still, while longtime Republican counties around Chicago, Detroit and Minneapolis swung hard toward Democrats during the Trump era, Milwaukee’s have moved much slower — in part, because they had a longer way to go.

“Waukesha County is changing, and it is not as red as it used to be,” said Brian Fraley, a Wisconsin Republican strategist. “The calculus is different now from what it used to be.”

Before Mr. Trump’s ascent, Waukesha County routinely gave two-thirds of its vote to Republican presidential candidates. But this year, Democrats have an ambitious target: 40 percent, a level none of the party’s presidential nominees have cracked since Lyndon B. Johnson in 1964.

The Democratic effort to cut into Republican margins in the county is part of a broader party strategy of losing by less in conservative areas.

For Mr. Trump, holding Ms. Harris below the 39 percent of the vote in Waukesha that Joseph R. Biden Jr. won in 2020 will be essential.

“If Waukesha County can get to 40 for Harris, numerically the G.O.P. is in massive trouble,” said Mike Hallquist, a Brookfield city alderman who is a rare Democrat elected to a local office in Waukesha County.

Mr. Fraley, the Republican strategist, predicted that Ms. Harris would win Brookfield, where he lives, and come close in Elm Grove, but he called the idea that Democrats would crack 40 percent countywide “a pipe dream.” Republicans, he said, would make up some of the margin lost with a stronger showing in the western, more rural part of the county, and in nearby Washington County.

Former Gov. Scott Walker, a Republican, said Brookfield and Elm Grove were going through the same political evolution that took place a decade ago in Wauwatosa, a Milwaukee County suburb that used to be a Republican stronghold and now reliably votes for Democrats. Such was the change that in 2020, Mr. Walker said, his old house had a sign in the yard for Mr. Biden.

“It’s part of this overall shift you see with blue-collar voters becoming more Republican and white-collar voters becoming more Democratic,” he said.

Still, Mr. Walker predicted that Mr. Trump would exceed 60 percent in Waukesha County because of his enduring strength in county’s western half.

Brookfield and Elm Grove have shifted to the left because their populations have grown younger and more diverse, even as educated suburbanites everywhere have abandoned Republican candidates in greater numbers. But some of the vestigial politics, and the social pressure to support Republicans, remain.

The path successful Democrats have taken in Waukesha has been to appeal to suburban, educated women who are now vital to the party’s fortunes across the country. The latest polling from The New York Times and Siena College found that in Wisconsin, Ms. Harris had an advantage of 17 percentage points over Mr. Trump among female voters, a gap consistent with her status in other states. Mr. Trump led among Wisconsin men by 15 points, the poll found.

Robyn Vining, a Democratic State Assembly member from nearby Wauwatosa whose district was redrawn this year to include Elm Grove and half of Brookfield, said she had organized her office and campaign to appeal and speak to women and their concerns. Some of her campaign signs say “Love Wins” in large font instead of her name, an indication of how she views her political message.

“You have to communicate with a woman who’s sitting on the floor nursing or bottle feeding a baby and watching a 3-year-old,” Ms. Vining said while canvassing an Elm Grove neighborhood on Saturday morning. “You have to know that that’s how much of her attention you get.”

One of the largest Democratic organizing groups in the area is an invitation-only Facebook group known as the Momma Dems, whose members — as Ms. Ruttum did for decades before planting her Obama sign — have vowed not to discuss the group publicly, to allow some members to keep their politics separate from their social, professional and, in some cases, family lives.

While polling suggests the presidential race in Wisconsin is effectively a dead heat, stories abound in the state’s Democratic circles about Harris voters who are unwilling to publicly say they support her for fear of creating conflict with Trump-supporting neighbors and family members.

“In Madison, everyone has a Harris sign,” said Representative Mark Pocan, a Democrat whose congressional district includes the state capital. Elsewhere, he said, “I hear the stories about supporters being afraid to tell anyone they are going to vote for her. I do think the silent majority is us this time and that’s going to make a difference.”

In Waukesha County, Democrats have made incremental gains in recent elections. Mr. Biden’s 39 percent was the highest margin for any Democrat in the county since Michael Dukakis drew the same level in 1988.

Last year, a liberal candidate for the State Supreme Court, Janet Protasiewicz, won 42 percent of the county’s vote on her way to a high-stakes victory for Wisconsin Democrats. This August, in a statewide referendum about legislative power over federal money that served as a proxy vote for the state’s parties, the Democratic-backed “No” side took 43 percent in Waukesha County.

Waukesha Democrats are not living under an illusion that they will win the county. Ben Steinhoff, 33, a Democratic firefighter running in a long-shot race for Waukesha’s congressional seat, said, “We know our role in this election.” But there is a giddiness that the days of Republican dominance may be over.

“We’re in a competitive area now,” said Sarah Harrison, a Democrat running for a Republican-held State Assembly seat in Brookfield. “I don’t know that it’s going to be solid blue. But I think we’re less maroon and more actual purple.”

Ruth Igielnik contributed reporting.