One rival, Senator Cory Booker of New Jersey, said pointedly this week that he was “getting calls from people who are Biden supporters who now want to hedge their bet” on the former vice president.

Ed Rendell, the former Pennsylvania governor and a Biden fund-raiser, acknowledged he had heard the anxieties. “They’re worried when they see only $9 million in the bank, because donors have a tendency to believe the person with the most amount of money wins,” said Mr. Rendell, who added that he does not share that view.

Mr. Schultz, the Biden campaign manager, said in an interview on Friday that Mr. Biden was facing a financial situation unlike any other Democrat: He is taking incoming fire from both the White House and primary opponents on a daily basis, and needs to play both offense and defense within the limits of $2,800 maximum donations.

“We can’t both do a general election and primary. And no one can,” Mr. Schultz said.