“I do not believe we’re a party at risk if they nominate me, and I do believe we’re a party at risk if we nominate someone who’s never held a higher office than mayor of South Bend, Ind.,” Mr. Biden said at a midday rally in Manchester.

Speaking with reporters Saturday afternoon, he repeatedly suggested that Mr. Buttigieg’s calls for change implied criticism of the Obama era. When pressed on whether his jabs at Mr. Buttigieg’s mayoral resume were comparable to Hillary Clinton’s swipes at then-Senator Obama during the 2008 primary — and if the remarks were an “act of desperation” — he bristled.

“Oh, come on, man!” he said. “This guy’s not a Barack Obama!”