As aides and allies watched Joseph R. Biden Jr.’s first debate performance last month, their initial optimism about his abilities turned to alarm as Senator Kamala Harris laced into him over race and busing.

It wasn’t just Mr. Biden’s halting answers that worried some of them. They thought he was showing his age — that, at 76, he appeared slow off the mark, uncertain about how to counterpunch as he allowed Ms. Harris to land clean hits without interruption.

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Within minutes, aides sent talking points to supporters titled “regarding the civil rights exchange,” and had information on his record ready for a late-night conference call. But his top advisers and other Democrats knew his unsteady response — ending with his listless comment that his “time is up” — would exacerbate questions about whether Mr. Biden, a veteran debater, was nimble enough to handle intense campaign moments or to beat President Trump on a debate stage next year.

“It felt like he was a step slow,” said Mike Lux, a Democratic strategist who was a top Iowa staffer for Mr. Biden during his 1988 presidential campaign and is so far neutral this cycle. “If Joe comes back strong in the next few debates, I think it’ll be fine. But I do think he looked kind of old in this debate.”