Allies of Joseph R. Biden Jr., concerned about his slipping poll numbers in the Democratic presidential primary and an onslaught of attacks from President Trump, are weighing whether to mobilize a super PAC supporting Mr. Biden and have held conversations with wealthy donors to gauge their interest in contributing money.

Mr. Biden and his campaign aides have said since the start of the race that they would not welcome an outside spending effort on his behalf, and every other major Democratic candidate has sworn off super PACs for the duration of the primary. A spokesman for Mr. Biden on Thursday reiterated that he opposed super PACs and would reject any such group that attempted to support him.

Yet several former staffers of Mr. Biden and political donors backing his candidacy have held conversations in recent weeks about moving ahead with a super PAC, and said Mr. Trump’s furious, and often unsubstantiated, allegations about the former vice president had convinced them it was imperative they act.

“For me, this week puts everything into stark relief,” said Larry Rasky, a former aide to Mr. Biden who is now a political fund-raiser and public relations executive. “And I was already thinking the campaign was being a little naïve about the resources we’d need to fight this.”