Jeanne Winograd, 72, a Democrat in Phoenix, is such a ride-or-die fan of President Biden that, on Valentine’s Day, she mailed him a card to say his vigor, not his age, would shape the presidential election. But after a week of panic attacks after his dismal debate performance, she felt compelled to send him another card.

This one said: Thanks for everything, but it’s time to go.

“I just love Biden, but he’s frail,” Ms. Winograd said. “Pass the baton.”

As Mr. Biden and his allies have scrambled to fix the damage from the debate last week, and to insist he will not bow out of the race, dozens of Democratic voters have said they no longer believe he can accomplish the one thing they urgently want — a defeat of former President Donald J. Trump. They are desperate for the party to find a Plan B.

In 80 interviews at Independence Day parades, pie-eating contests and political events this holiday in the political battlegrounds of Arizona, Michigan, Wisconsin and North Carolina, more than half of voters who had supported Mr. Biden in 2020 now said he should drop out of the race. About a quarter said he should stay in. The rest were unsure.

The turmoil engulfing the Democratic Party had left them sleep-deprived and divided about a path forward, with some saying it would be pragmatic to dump Mr. Biden and others arguing that he was Democrats’ best — or only? — option in November.

Several voters said Vice President Kamala Harris was the smartest replacement for Mr. Biden. But others worried she could not match Mr. Trump and mentioned that the Democratic governors of Michigan or Pennsylvania might be a smarter choice. What about one of the Castro brothers from Texas, one voter suggested? Another asked, What about Michelle Obama?

Every voter but one said they would still vote for Mr. Biden if he remained in the race. They said they viewed Mr. Trump as a greater threat to democracy, women’s rights and the future of the world than Mr. Biden, who would be 86 at the end of second term. They also said that they believed that Mr. Trump, 78, was not mentally equipped to serve another four years.

Some also worried about the risks of abruptly replacing a presidential candidate four months before an election, and the growing sense that the party did not know what to do.

“We can’t agree on a way ahead, we can’t agree on what to do about the current situation,” said Raja Seshadri, 46, who works at the National Institutes of Health in Raleigh, N.C. “We’re going to lose.”

The willingness of Democratic voters to publicly contemplate cutting Mr. Biden loose stands in sharp contrast to what they are hearing from their own leaders.

While two sitting congressional Democrats have called for Mr. Biden to step aside, a vast majority of Democratic elected officials rallied to support him this week, even as a new poll by The New York Times and Siena College showed Mr. Trump opening a six-point lead over Mr. Biden among likely voters.

Some voters said they felt frustrated and betrayed by their party’s efforts to short-circuit any discussion about whether Mr. Biden should step aside. They said Mr. Biden’s meandering answers during the debate could not be explained away as a bad night, or the product of jet lag or a cold, and that they were not reassured by his appearances at events afterward.

“It is disgraceful they’ve allowed him to get here and all of us to be here,” Elaine Becherer, a 48-year-old who works in university planning in Phoenix, said as she and other Biden voters in Arizona discussed his candidacy on a video call this week.

“Our ‘Dear Leader,’ ” Cristina Ospina, a 56-year-old neurologist in Phoenix who studies movement disorders, chimed in sarcastically, referring to North Korea’s adulatory description of its leader, Kim Jong Un.

Frustrated, some Democratic voters have begun airing their concerns in the open.

Some said they wrote letters to the White House and reached out to local elected officials. In Traverse City, Mich., Greg Holmes, 71, a retired psychologist and a loyal Democratic voter, showed up to a campaign appearance by the first lady, Jill Biden, holding a sign that said, “Step Aside Joe!”

“If Biden says and does what I call the right thing, or courageous thing, and passes the baton, I will be ecstatic and fired up for the next person,” Mr. Holmes said. “Because I think Trump really represents a terrible, terrible threat to our democracy.”

Mr. Holmes said he did not believe Mr. Biden was fit to serve as president, and that he did not believe the Democratic Party and the Biden campaign had been honest with voters. At this point, he said, the best course of action would be for Mr. Biden to release his delegates to the Democratic National Convention and let them settle on a new nominee.

In the heavily Democratic Milwaukee suburb of Wauwatosa, the Biden campaign’s troubles were not far from many voters’ minds as they watched bagpipers and high-school dance teams march in the city’s annual Independence Day parade.

“He should exit the race,” said Gerry Ford, a 72-year-old engineer (and not the 38th president of the United States). “The sooner the better. He doesn’t meet the criteria for having the most important job in the world.”

Mr. Ford also said the White House and the Biden campaign had not been transparent after the debate.

“It fulfills all of our suspicions about politicians that they can’t be straight with voters,” he said. “It’s embarrassing for the country.”

Down the street, Sophia Artus and Emma Due, who are both 18, said they did not feel enthusiastic about either presidential candidate in the first votes of their lives. They had been so dispirited by the debate that they turned it off halfway through. They said they would likely vote for Mr. Biden, but only because he was not Mr. Trump.

“Kamala Harris would carry the torch, and she’s better than Trump,” Ms. Due said. “There’s a lot of new ideas that younger people express, but it’s not reflected in our candidates.”

Other Democrats have decided to swallow their concerns and stick with Mr. Biden.

Melissa Wicksel, 21, of Raleigh, N.C., said that defeating Mr. Trump was so imperative that Democrats needed to rally around Mr. Biden and highlight his policy achievements. She said her Democratic friends had also expressed their support for Mr. Biden.

“He has a stutter, he is older, that’s no doubt, but overall, if you listen to what he says, I understand him,” Ms. Wicksel said. “Trump, on the other hand, just lies the whole time.”

Liz Purvis, the chair of the Granville County Democratic Party in North Carolina, a purple county that Mr. Trump won in 2020, said her thought on the intraparty debate right now is simple: “Straight up, I think sticking with Biden is the right call.”

“With the money they’ve raised, and the organizing power that the coordinated campaign is doing, our smoothest road toward a Democratic victory feels to me like it runs through a Biden campaign,” Ms. Purvis said.

She added that “it feels like the infighting is not forward momentum, and what we need is forward momentum.”

In Tempe, Ariz., Michael John, 35, said he had decided to cast his first vote this November after starting his own small business, Navajo Mike’s, making fry-bread mix and barbecue sauce. He realized how deeply politics was intertwined with his life, family and success. Mr. John, a Navajo citizen, said that Mr. Biden has been supporting Native-owned businesses like his with loan guarantees and help with marketing and business development. But he also said he thought Mr. Biden should ease out of the race to avoid a loss to Mr. Trump.

“It would be ideal to have someone more coherent and involved, and there,” he said, adding that President Biden should “go do something, cool, fun. You don’t need the weight of the world on you.”

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