As the vice president thinks, he is also laying groundwork. He attended a pre-inaugural party with Democrats from Iowa, the first caucus state, and invited the governor of New Hampshire, the first primary state, to his private swearing-in ceremony. In two other likely early primary states, he will address the Democratic State Convention in South Carolina next month and appear at a testimonial for the retiring Senator Carl Levin in Michigan. He is enlisting candidates and collecting money for midterm elections.

“He is already generating lots of good will among House Democrats and Democratic candidates across the country,” said Representative Steve Israel of New York, the chairman of the Democratic Congressional Campaign Committee. “He is diving into races. He is making recruiting calls. He is fund-raising. He is firing up our core supporters across the country.”

Aides said Mr. Biden would do those things regardless of his own ambitions. And the preliminary moves do not address the more fundamental challenge: How would he run against Mrs. Clinton, who seemed to be Mr. Obama’s anointed heir in a joint interview they gave to the CBS program “60 Minutes” earlier this year? Mr. Biden would not have exclusive claim to the Obama legacy and, like any vice president, he would need to distinguish himself from the departing president. He could run to the left of her, emphasizing a more populist approach. Or he could run as the insurance policy in case she does not run or if she falters.

It is not clear that a presidential campaign makes sense for Mr. Biden, who would turn 74 shortly after the 2016 general election and 82 before the end of a second term.

But it is in his interest to keep the option open as long as possible to maintain his influence and to see what Mrs. Clinton decides to do. The moment Mr. Biden declares he will not run, he becomes a lame-duck No. 2 in a lame-duck administration.