Representative Cedric Richmond, Democrat of Louisiana, a Biden backer and a recent chairman of the Congressional Black Caucus, said that Mr. Obama was “still very, very significant for African-American voters,” and that other candidates were misrepresenting history as they try to win over black Democrats.

Mr. Richmond added that it was “hypocrisy” for Mr. Bloomberg and Mr. Sanders to run ads saying they were “BFFs” with Mr. Obama “after refusing to help out Obama when he needed them.”

A Biden adviser, speaking on condition of anonymity to discuss campaign strategy, said the campaign’s view was that the attacks on Mr. Sanders over Mr. Obama were less likely to have an impact than the campaign’s criticism of Mr. Bloomberg, who is not on the ballot in South Carolina. Mr. Sanders, the person said, has locked in many of his supporters, but Mr. Bloomberg, a former Republican who could siphon off moderate support in Super Tuesday states, is more vulnerable to charges of disloyalty.

Mr. Sanders, for his part, has repeatedly said that he views Mr. Obama as a historic “icon” with whom he had policy disagreements, and has insisted he never planned to challenge him.

But aides who worked for Mr. Obama’s re-election campaign said they believed the threat was real and had fueled fears that such a challenge could sap much-needed support from the party’s progressive wing. “He should be held accountable,” Patrick Dillon, a senior adviser to Mr. Obama’s 2012 campaign aide, said of Mr. Sanders. “It was clear he was up to something.”

Mr. Sanders and Mr. Obama, while not close, are on amiable terms, and the senator has called the former president in recent weeks to update him on his campaign, and to keep their lines of communication open, according to aides to both men.

Mr. Obama, in turn, has expressed admiration for Mr. Sanders’s tenacity and small-donor fund-raising operation and his political acumen, but he has also acknowledged the magnitude of the challenge of getting other Democrats to fall into line quickly behind Mr. Sanders if he wins, a person in his orbit said.