The television commentators on the ballroom’s giant screen — the ones questioning whether President Biden should be the Democratic nominee this fall — had been muted. A D.J. had been firing up the crowd, and a crush of Democrats had thickened along barricades, readying for selfies and handshakes.

Mr. Biden’s campaign was on the defense in many corners after his debate on Thursday night with former President Donald J. Trump. But as midnight approached in a windowless ballroom at a Hyatt Regency in Atlanta, where supporters watched the debate and then received Mr. Biden and his wife just after it ended, just about everything, it seemed, had gone perfectly fine.

“Joe, you did such a great job,” Jill Biden, the first lady, gushed as she turned toward her husband less than 30 minutes after he had left the debate stage. “You answered every question. You knew all the facts.”

For his part, Mr. Biden spent no time dwelling on his showing. He preferred to talk about the performance of his adversary, Mr. Trump.

“I can’t think of one thing he said that was true,” Mr. Biden said of his rival. He turned to the familiar notes of a campaign: “We’re going to beat this guy. We need to beat this guy, and I need you in order to beat him.”

As he later made his way through a sea of smiles, the ballroom served, at least for a time, as presidential cocoon.

In the hours before the debate, these Biden supporters were in buoyant spirits. And through the 90-minute debate, even as the hall’s acoustics sometimes made it difficult to hear much of anything, they sporadically jeered Mr. Trump. They roared when Mr. Biden, more than 40 minutes into the debate, cited Mr. Trump’s 34 felony convictions.

Still, the star of this party wasn’t actually the debate, but what everyone in the room knew was to come afterward: a visit from a sitting president.

As the debate neared its end, the most insistent, campaign-ready chants rumbled through the ballroom for a brief spell.

“Let’s go, Joe!”

By then, in Washington and elsewhere, some powerful Democrats were raising concerns about Mr. Biden’s halting performance. A handful of veterans of Georgia Democratic politics looked on impassively. The D.J. came to the stage.

And, soon after, so did Mr. Biden. He vowed to fight on, and he savored the glow, shaking hand after hand. Later in the night, during a stop at a Waffle House on his way to the airport, Mr. Biden brushed off word of Democrats’ misgivings, saying, “I think we did well.”