“Nothing is guaranteed,” said Anthony Daniels, the state House minority leader in Alabama, a Super Tuesday state where Mr. Biden is hoping to have a muscular showing early next month. “People want to know that whoever the candidate that is chosen can go the distance.”

Mr. Biden has sought to keep expectations low in New Hampshire, going so far as to say in a debate on Friday night that he would “probably take a hit” in Tuesday’s primary.

And there are already signs that he is eager to move on.

On Monday, Mr. Biden held a phone call with top South Carolina supporters in which he expressed excitement about visiting the state, which has a predominantly black electorate in Democratic primaries, and promised to be there soon, according to people on the call. They added that he and a senior adviser, Symone D. Sanders, had both suggested that the race for the nomination would be heavily influenced by the outcome of the Feb. 29 primary in South Carolina, a state that is more representative of the party and that stands in contrast to heavily white Iowa and New Hampshire.

Yet a damaging loss in New Hampshire could put constraints on the resources Mr. Biden will have available to compete in subsequent contests. Several donors and other Democrats inclined toward Mr. Biden have privately expressed jitters about a fourth-place finish or worse in New Hampshire, and are closely watching the result. Another weak outcome, after Mr. Biden’s fourth-place finish in the Iowa caucuses, would be alarming, some have said.