The job was to spin, and they had their work cut out for them.

In the minutes after the presidential debate ended on Thursday night, a cluster of Democrats walked into the spin room to defend their candidate, an 81-year-old president who showed up after a week of debate preparations with a hoarse voice, a head swimming with facts and figures, and an inability to contain the reality-bending and often fact-free bluster of his opponent, Donald J. Trump.

For much of the debate, Mr. Biden looked down, or looked wide-eyed and slack-jawed, absorbing what was happening, angry but unable to hit back. At times he spoke into a microphone that had been cut off according to debate rules his team had outlined.

So it was a bit of an uphill climb. The crew had the difficult job of trying to promote the policies the president tried but often failed to espouse, without calling attention to the one thing Mr. Biden could not outrun: his age.

“I would never turn my back on President Biden’s record,” Gov. Gavin Newsom of California said, when asked whether he supported the whispers — swiftly rising to a shriek — among some Democrats who believed Mr. Biden’s performance was bad enough to warrant being struck from the ticket. He added: “I was very proud of the president.”

And on went the sober scene among the small clutch of surrogates, who were all clearer messengers for the president’s policies than Mr. Biden himself had been over the course of more than 90 minutes onstage.

The Trump side beat them to the floor by several minutes, and at least a dozen surrogates were swaggering. Lara Trump, the co-chairwoman of the Republican National Committee, said that, from what she had seen, “it was very clear” that the theme of the debate was “strength versus weakness.”

She skated over questions from reporters about her father-in-law’s attempts to rewrite history about his actions during the Jan. 6, 2021, attack on the Capitol.

In the other corner, Mr. Newsom and Mary Trump, a niece of Mr. Trump who has become an outspoken critic, were flanked by Rep. Robert Garcia of California, Rep. Jasmine Crockett of Texas and Sen. Raphael Warnock of Georgia. Each of them looked stone-faced as they listened to one another attack Mr. Trump.

Mr. Newsom was asked whether he would accept the party’s nomination if it came to that. “I would never turn my back on President Biden,” he repeated.

Not exactly a no.

Ms. Trump, who wrote a book in which she alleged that her uncle had long embraced “cheating as a way of life,” stayed quiet and looked at the floor when she was asked whether Mr. Biden’s performance had made her nervous.

“People can choose between a con in chief and a commander in chief,” Ms. Crockett said. “What we saw was someone who sat up there and was acting as if he was some used car salesman that wanted to just tell us whatever and pretend as if it was fact. The reality is that our president submitted to you what looks like substance.”

Mr. Trump’s vice-presidential hopefuls, meanwhile, unfurled across the room like it was a bizarro-world beauty pageant, minus the sashes.

The contestant from North Dakota, Gov. Doug Burgum, greeted reporters and hailed the night as a win for Mr. Trump, as did Senator Marco Rubio of Florida and Ben Carson, who served as Mr. Trump’s secretary of Housing and Urban Development.

Nearby, Mr. Biden’s old friend Senator Lindsey Graham of South Carolina stared gravely into the glare of cameras. He hated to say it, he said, but he worried that Mr. Biden was not fit to be commander in chief for the next six months, let alone for the next four years.

“I’m worried that we have a situation in the world where the president seems to be compromised,” Mr. Graham said. “What we saw tonight was a man who was more confused than not. The bad guys are watching, too.”

Corey Lewandowski, an adviser to Mr. Trump who has orbited around the former president for years and flew to Atlanta aboard Mr. Trump’s plane, said that Mr. Trump “put together coherent sentences” while Mr. Biden “looked out of his depth.”

In a ballroom across town, patrons of a debate-watch party waited for Mr. Biden to appear and do some spinning of his own.

The first lady, Jill Biden, praised her husband for answering the questions he was asked. Mr. Biden said that his opponent had lied the whole way through.

“I can’t think of one thing that he said was true,” Mr. Biden said. He focused more on Mr. Trump’s performance than his own.

“We’re going to beat this guy,” Mr. Biden said later. “We need to beat this guy. And I need you to beat him.”

The crowd responded, “We need you!”

At a Waffle House after the debate, Mr. Biden briefly spoke with reporters, telling them his hoarse voice was because of a sore throat. He said he had felt he had done well.

“It’s hard to debate a liar,” the president said.