President Biden knew immediately after stepping off the stage in Atlanta on Thursday night that the debate had gone wrong. In those first stricken moments after a raspy, rambling and at times incoherent performance, he turned to his wife, Jill Biden.

Whatever was going to happen next in Mr. Biden’s last presidential race, after perhaps the worst moment of his long political life, was always going to come down to her. His wife of 47 years had entered his life all those decades ago, reluctant to get into politics but fully embracing his dreams and his belief that he would one day reach the White House.

Now, her 81-year-old husband looked at her after a disastrous 90 minutes onstage.

The first lady’s message to him was clear: They’d been counted out before, she was all in, and he — they — would stay in the race. Her thinking, according to people close to her, was that it was a bad night. And bad nights end.

“To say they’ve been in foxholes together doesn’t even begin to explain their bond,” said Elizabeth Alexander, the first lady’s communications director, who has been with Mr. Biden since his Senate days.

So Dr. Biden spent the 24 hours after the debate putting her decades as a political spouse to the test, projecting confidence and normalcy while effusively praising her husband. But, like the president, she is an intuitive political messenger who can sense the mood of a crowd. She knows that along with the cheering supporters, there are legions of people suddenly accusing her of forcing an old man to put one weary foot in front of the other.

If Mr. Biden were to seriously consider departing the race, allowing a younger candidate to replace him, the first lady would be the most important figure — other than the president himself — in reaching that decision.

“Jill is the final and most important voice. She knows him and loves him with a passion. She also knows everything about him. Most big decisions are made with Valerie and Jill in the end,” said John Morgan, one of Mr. Biden’s top donors, referring to the president’s younger sister, who has run nearly all of his political campaigns.

Indeed, as major Democratic Party donors connected Friday, by text, by phone or in person, one of the most immediate questions they asked one another was whether any of them knew how to get a meeting or a conversation with the first lady.

After nearly a half-century in politics, the Bidens view themselves as long-game people. And right now, neither wants the story of the president’s long political career — one defined by tragedy, resilience and unceasing ambition — to end on a stage in Atlanta, across the podium from former President Donald J. Trump, a man they both revile.

“He wants to win and she wants that for him, and for the country,” Ms. Alexander said. “She’s his biggest supporter and champion, because she believes in him, and she fears for the future of our country if it goes the other way.”

In front of supporters on Friday, the first lady embraced the talking points espoused by Democratic Party leaders, including the vice president, Kamala Harris, that Mr. Biden’s bad performance did not erase years of successful legislating.

“As Joe said earlier today, he’s not a young man,” Dr. Biden told a group of donors assembled in Manhattan on Friday afternoon, her third stop since leaving Atlanta. “After last night’s debate, he said: ‘You know, Jill, I don’t know what happened. I didn’t feel that great.’ I said, ‘Look, Joe, we are not going to let 90 minutes define the four years that you’ve been president.’”

Dr. Biden understood that the debate night had amounted to a serious misstep. The president had needed to walk into the debate hall and address concerns about his age. Instead, he walked onstage after six days of preparations and mock debates at Camp David and had little other than a raspy voice to show for it. (The White House said he had a cold.)

She listened as Mr. Trump mocked him. “I really don’t know what he said at the end of that sentence,” Mr. Trump said when Mr. Biden blundered an answer on immigration. “I don’t think he knows what he said either.”

She listened as the former president attacked Hunter Biden, Mr. Biden’s son whom she had raised since childhood and had stood by during a recent trial on gun charges, sitting front row in the courtroom as the worst moments of his addiction were recounted for the world to see.

And she watched as her husband looked wide-eyed and slack-jawed as Mr. Trump went on, angrily absorbing what was happening but largely unable to hit back.

Afterward, Dr. Biden held hands with the president, who walked gingerly down the stairs. The moment quickly went viral. At a campaign-organized watch party the Bidens visited shortly after the debate, she praised her husband for his performance. But critics elsewhere saw her giving him a virtual pat on the head for simply making it through the debate.

“You answered every question, you knew all the facts,” she said. “And what did Trump do?”

“Lie!” the crowd shouted.

Suddenly, a first lady who had skirted major controversies over the past three and a half years found herself in the cross hairs of people who believe she has been trying to hide his diminished faculties.

“What Jill Biden and the Biden campaign did to Joe Biden tonight — rolling him out on stage to engage in a battle of wits while unarmed — is elder abuse, plain and simple,” Representative Harriet M. Hageman, Republican of Wyoming, wrote in a social media post.

The Drudge Report, a prominent conservative-leaning website whose author, Matt Drudge, has soured on Mr. Trump, ran an unflattering photo of the Bidens on Friday with the headline “CRUEL JILL CLINGS TO POWER.”

The first lady and her advisers have long noticed similar claims on conservative websites, and are aware that they are leaking into the mainstream. Ms. Alexander said Dr. Biden views her “amorphous” role as “an act of service, rather than some mythical power grab invented by the dark corners of the internet.”

She added that the first lady sometimes felt hamstrung by the demands of the role, one rife with expectations and hidden trip wires.

“You have to be supportive, but not so supportive that your motives are questioned,” Ms. Alexander said, placing much of the blame on the internet, bots and a right-wing machine that fuels “every conspiracy.”

Advisers to the president and first lady downplay the idea that she has the ability to unilaterally pull the plug on the president’s re-election campaign and clear the way for another candidate four months before a presidential election. They acknowledge her unique influence and power in his life, but they say Mr. Biden is in control of his own campaign.

“There’s too much putting this on Jill,” said one of Mr. Biden’s top advisers, who spoke on the condition of anonymity to discuss a family dynamic. But as long as Mr. Biden wants to run, advisers say, she will support him.

“When Joe gets knocked down, Joe gets back up,” she told the donors in New York. “And that’s what we’re doing today.”