They started the night hoping that President Biden would use the first debate of 2024 to his advantage, that he would finally quash fears about his age and give the impression of a determined statesman compared with former President Donald J. Trump.

But for the roughly 40 Democrats who gathered Thursday night at a union hall in Sacramento, it did not take long for the mood to descend into something between grim despair and mild panic. Within minutes, even ardent supporters in the capital of California fell silent, exchanging glances and acknowledging quietly that Mr. Biden, his virtues aside, seemed less forceful than Mr. Trump, and weary. Toward the end, some of the younger attendees left before the debate was over.

“Neither of them inspires confidence,” said Dubrea Sanders, 25. “It’s going to be a very scary November for a lot of people, including myself.”

The crowd, mostly state workers, policy analysts, labor activists and members of a local Young Democrats organization, cheered from white folding chairs when the president took the stage and heckled Mr. Trump’s false claims, roaring with laughter as Mr. Trump mispronounced “China” and talked about “immaculate water.”

But the frailty in Mr. Biden’s voice gave them pause.

“Have you seen Twitter?” winced Nancy Van Leuven, 72, a retired media and communications professor, pointing to early criticism of Mr. Biden’s performance. “The thing is, Biden looks older. And Trump is still resolute; even if he’s not telling the truth, it still looks believable.”