Mr. Biden has been in contact with donors who could help finance a campaign, eyeing major contributors to President Obama and pillars of his own fund-raising network: trial lawyers, Jewish leaders and Greek-Americans. On Thursday, the vice president, who is not known for aggressively courting donors, spoke to George Tsunis, a Long Island developer and longtime supporter, who raised more than $750,000 for the Obama-Biden ticket in 2012.

“I think he is doing the prudent thing, which is to look at it and lay down some groundwork should he run,” said Mr. Tsunis, saying that Mr. Biden is aware that Mr. Tsunis will help him if he enters the race.

At the same time, some Democrats supporting Mrs. Clinton have quietly signaled that they would re-evaluate their support if Mr. Biden joined the race. For example, Tom Daschle, an influential former Senate Democratic leader who has given the maximum amount allowable to Mrs. Clinton’s campaign, has indicated that he would reassess his position if Mr. Biden entered the race, according to people who have been in contact with him in recent days…

“He’s not unrealistic that if she’s able to right the ship here, at this point it’s tough, really tough, to see a lot of Democrats coming off her,” said one former senior Obama administration official who recently discussed the merits of a campaign with Mr. Biden. “On the other hand, the things with the emails and everything else could deteriorate — who knows? So I think he’s figuring he’s got another month or so to see what happens, to sort of put feelers out there.”