For years, President Biden has had a ready retort for the naysayers who have questioned his facility and fitness to run for president again at age 81 and to serve until he is 86. “Watch me,” he has said.

But in the days since tens of millions of Americans watched him fumble Thursday’s debate in real time, Mr. Biden has essentially adopted a new line: Trust me.

“Folks,” he said at a New York fund-raiser the next night, “I would not be running again if I did not believe with all of my heart and soul that I can do this job.”

It’s a cliché of political strategy that smart campaigns meet voters where they are. That typically means fashioning a strategy that taps into the public’s pre-existing feelings, rather than seeking to change how the electorate perceives matters.

Yet the trouble for the president is that even on the eve of his faltering debate, a New York Times/Siena College poll showed that 69 percent of voters — and 55 percent of Biden voters — saw Mr. Biden as too old to be an effective president. It is not a new concern: Nearly two years ago, a strong majority of Democratic voters said they wanted a new standard-bearer.

Now those persistent concerns from everyday Americans are being echoed publicly by many in the Democratic Party’s pundit class and privately by lawmakers, donors and strategists. They are worried about losing a 2024 campaign against former President Donald J. Trump, whom many view as an existential threat to the nation.

“Biden’s debate performance was a catastrophe from which there may be no recovery,” one House Democratic lawmaker texted a Democratic donor, Whitney Tilson. Mr. Tilson, a former hedge fund manager, shared the message on the condition the lawmaker not be named.

Around Mr. Biden, a siege mentality has set in for a team that remembers — and is fond of repeating — how it outlasted the doubters four years ago to win the nomination in the first place.

“He’s really at his best when the pundits are overreacting and counting him out,” Ted Kaufman, one of Mr. Biden’s closest advisers and his former chief of staff in the Senate, said in an interview. “He has a hell of record. I think he should stay. He is the best president in modern history.”

As the president huddled with his family at Camp David in recent days, his advisers rushed to keep in line any potential prominent wayward Democrats who might abandon their party’s leader. Mr. Biden’s team was discussing some kind of interview or news conference to comfort the concerned even before Mika Brzezinski, the co-host of the MSNBC show Mr. Biden often wakes up to watch, said in a monologue on Monday that “America needs an explanation from Joe Biden and reassurance that the other night was a onetime event.”

On Monday night, Mr. Biden returned to the White House and addressed a Supreme Court ruling on presidential immunity. He spoke for five minutes with the aid of a teleprompter and did not take questions.

This spring, Mr. Biden’s top brass pressed for the earliest general-election debate in history, as a way to force voters to sooner accept the reality of a Trump-Biden rematch that polls have repeatedly showed they do not want. It was a calculated gamble at a moment when Mr. Biden trailed in the polls. The thinking at the time: Once that contrast became clearer and the contest undeniable, those on-the-fence Democrats would rejoin the party fold.

Instead, the debate flop has ignited a fresh round of questions about whether Mr. Biden should stay atop the ticket. At the least, it has prolonged the very conversation his team had hoped to extinguish.

“The gift Joe Biden gave us was agreeing to a debate before the convention,” said Jon Favreau, a former speechwriter for President Barack Obama and the co-host of the popular progressive podcast Pod Save America who has called for the party to consider replacing him. “If the debate was in October, I would be holding my tongue.”

Mr. Favreau said the Biden camp’s attempts to silence the second-guessers were insulting to voters.

“Guess what — millions of Americans saw that,” Mr. Favreau said of the debate, “and you can’t just tell people who are criticizing that they’re bed-wetters and crazy.”

On the Democratic National Committee’s call for members over the weekend, the party chairman, Jaime Harrison, spoke while everyone else was on mute. It felt to some like a too-on-the-nose metaphor for party leadership’s lack of desire for genuine grass-roots feedback.

The Biden campaign sees the $26 million in grass-roots donations and volunteer sign-ups that tripled the usual rate as evidence of voter support post-debate.

In recent days, Mr. Biden has more frontally acknowledged his flaws — and not just on the debate stage, saying that he didn’t “walk as easy as I used to” or “speak as smoothly as I used to.”

“The voters don’t want gaslighting and pretending Biden is more than he is,” Mr. Khanna said. “He was brutally honest about who he is.”

Some attention has centered on the role of the first lady, Jill Biden. Her assistance to her husband as he tried to descend a step after the debate went viral, as did her post-debate praise at a rally (“Joe, you did such a great job!”). On Monday, Vogue unveiled its newest cover, featuring Dr. Biden wearing a $5,000 white Ralph Lauren tuxedo dress alongside the words: “We will decide our future.”

Michael LaRosa, a former adviser to Dr. Biden, said those expecting her to urge her husband to step aside fundamentally misunderstood their political relationship. He said it was a partnership forged in part by Mr. Biden’s early exit in the 1988 presidential race after a plagiarism scandal.

“In 1987, she saw him be forced out by the press, pundits and polls, and it was really a scarring experience for both of them,” said Mr. LaRosa, who said he had discussed the 1988 episode multiple times with the first lady when he worked for her. “I think they learned from that experience and they weren’t going to have their hands forced like they were in 1987.”

The Bidens, Mr. LaRosa explained, view Mr. Biden’s life and career as a tale of overcoming adversity. “This is another chapter of resilience in what is the story of Joe Biden,” he said, summarizing how he believed they would see it.

Indeed, the Biden campaign’s first post-debate ad closed with Mr. Biden declaring, “When you get knocked down you get back up.”

Any serious reckoning inside the party about Mr. Biden’s age was put on ice after the 2022 midterm elections, when Democrats outperformed expectations. The White House took it as validation of its political strategy — and of the limitations of studying the president’s sagging approval ratings for clues to the outcome of elections.

“My intention is that I run again,” Mr. Biden said the next day.

And that was that.

Mr. Biden has visibly aged, as most presidents do. But as early as late 2021, the White House physician had noticed a change, observing more frequent and severe “throat clearing” and a gait that was “perceptibly stiffer” than a year earlier. He recommended “shoe orthotics.”

Mr. Biden’s handlers insisted he could handle a re-election campaign even as their handling of him gave hints otherwise. He began using the shorter stairs to board Air Force One after his tripping went viral. He has done fewer news conferences than his predecessors. He passed on a pregame Super Bowl interview. His events have become intentionally shorter, too.

And after a special counsel’s report laced into his mental acuity in ways the White House saw as gratuitous — tagging him as a “well-meaning, elderly man with a poor memory” — Mr. Biden called an evening news conference to rebut that caricature, only to flub a reference to the president of Egypt, calling him the president of Mexico instead.

In the wake of the debate, senior Biden officials are making the case privately that switching candidates would be unrealistic, risky and chaotic. And in a fund-raising message, Rob Flaherty, a deputy campaign manager, explicitly argued that any alternative would “be less likely to win than Joe Biden.”

Some of the Democratic Party’s future leaders urged voters to stand by Mr. Biden.

“We’ve got to have the back of this president,” Gov. Gavin Newsom of California said on MSNBC in the spin room after the debate. The next morning, Gov. Josh Shapiro of Pennsylvania went on MSNBC and said, “Stop worrying and start working.”

Privately, Democratic strategists worry about asking voters to work for Mr. Biden rather than the other way around.

In a sign of the campaign’s aversion to risk, the two senior-most Biden advisers who went on television over the weekend to defend the campaign — the White House adviser Anita Dunn and the pollster Molly Murphy — joined MSNBC shows anchored by former Biden advisers.

“What’s behind Door No. 2 is always going to have some appeal,” Ms. Murphy said, dismissing surveys showing voters wanting another nominee.

And yet 80 percent of Republicans in the most recent Times/Siena poll said they wanted Mr. Trump to remain the nominee, even after his felony convictions, a figure far larger than the share of Democrats who wanted Mr. Biden.

For now, the Biden campaign has renewed a fight with a favorite foil: the media.

“Did you see the awesome clips of our supporters on the tarmac doing the Cupid Shuffle at 2am on the night of the debate?” read a Biden fund-raising email from the weekend. “Well, no, probably not, because the media is busy hyperventilating and trying to manifest drama to boost ratings.”