WASHINGTON — As President Obama reviewed the comedy routine he was to deliver at the recent White House Correspondents’ Association dinner, one joke struck him as too hot. It suggested he might dump Vice President Joseph R. Biden Jr. from the ticket.

“Four years ago, I chose Joe Biden as my running mate,” Mr. Obama was to say, according to people familiar with early drafts of the planned remarks. “Four years later, I’m almost positive I’m going with Joe again.” He would then affect an exaggerated wink for the audience. But the president instructed his speechwriters to cut the line, figuring it would only inflame speculation from Beltway busybodies about his vice president’s standing.

Mr. Biden is also a bit raw on this topic. It goes to an essential insecurity that haunts almost every No. 2 — a job that the backslapping, shoulder-squeezing, muscle-car-loving Mr. Biden was wary of in the first place.

Mr. Biden, 69, delights in speaking bluntly — even as that can complicate things for the White House, as it did Sunday when Mr. Biden said he was “absolutely comfortable” with same-sex marriage (an endorsement that went beyond Mr. Obama’s statements on the issue). He loves to remind people that he did not have a boss for 36 years in the Senate, where he prided himself on being “my own man.” He would tell aides and Senate colleagues that “my manhood is not for sale” if he felt pushed around. He told friends he feared that the vice presidency could be “emasculating.”