Vice President Biden listens as President Obama speaks in the East Room of the White House in Washington. (Andrew Harnik/Associated Press)

The possibility that Vice President Biden may jump into the 2016 presidential campaign is convulsing the network of wealthy Democrats that financed President Obama’s two White House bids, galvanizing fundraisers who are underwhelmed by Hillary Rodham Clinton’s performance.

A wide swath of party financiers is convinced that Biden will make a late entry into the race, and a sizable number are contemplating backing him, including some who have signed on with Clinton, according to more than a dozen top Democratic fundraisers nationwide.

Their potential support — driven in part by a desire to recapture the passion they felt in Obama’s campaigns — could play a key role in helping the vice president decide whether to make a third White House bid. The chatter among a cadre of well-connected party fundraisers suggests that he could benefit from an early jolt of money should he run.

Clinton maintains a broad and loyal donor base, and her financial dominance would present a huge challenge for Biden if he entered the campaign this fall. The former secretary of state amassed a record $47 million during her first quarter as a candidate and is flanked by an array of super PACs and other independent allies socking away millions for her.

Biden would face a tight scramble to raise money this far along on the calendar. Because donors can give a campaign only up to $2,700, he probably would have to lean heavily on a super PAC, which could accept unlimited sums, a move that would be distasteful to many liberal voters.

Although Biden has not built his own fundraising network, he developed relationships with donors around the country as Obama’s running mate. And there is growing unease among some of Obama’s biggest financial backers about the controversy over Clinton’s use of a private e-mail server while she was secretary of state.

Many of the president’s fundraisers are still up for grabs. Of the 770 people who collected checks for Obama’s 2012 reelection bid, just 52 have signed on as a “Hillblazer” bundler for Clinton or have held a fundraiser for her, according to a Washington Post analysis.

Top Democratic money players — many of whom spoke on the condition of anonymity to describe private conversations — said discussions among senior Obama fundraisers about Biden’s possible bid have taken a serious turn in the past few days.

The news that former Obama administration officials Anita Dunn and Bob Bauer met privately with the vice president Monday night further accelerated a sense of movement toward Biden. Dunn and Bauer declined to comment.

“I think you are going to see a groundswell,” said one prominent party funder, who said that top political aides and fundraisers who backed Obama in 2008 and 2012 are considering helping the vice president. “There is a lot of enthusiasm on the wires. This feels real.”

Kirk Dornbush, a San Francisco biotechnology executive who helped lead Obama’s fundraising in the South and has not signed on with the Clinton campaign, said Biden would find a receptive audience among the president’s bundlers.

“Obama donors, the whole Obama world just loves Joe Biden — just loves Joe Biden,” said Dornbush, whose father served as President Bill Clinton’s ambassador to the Netherlands. “And so they would be very open to sitting down with him and having the conversation, if not writing him a check.”

He added, “That having been said, people will want to look him in the eye and see that in fact he has the fire in the belly, because that was just crystal clear when we all had that conversation with then-Senator Obama, and I think people want to have that same sense with Joe.”

Jon Cooper, who was an Obama bundler and is now the national finance chairman for the Draft Biden 2016 super PAC, said he is fielding increasing interest from fundraisers he worked with during the past two presidential campaigns. Nearly a dozen of the 35 bundlers Cooper contacted have committed to helping if the vice president runs, according to the Long Island technology manufacturer.

“It’s getting a lot easier to get people to return my phone calls, because there’s a greater feeling among big donors that this really could be happening,” Cooper said. “There is going to be a deep reservoir of support, particularly among Obama fundraisers and bundlers, if Joe Biden enters the race.”

Even donors who are committed to Clinton say they expect that many fellow fundraisers would jump to Biden — particularly those who think they would be bit players in the massive fundraising operation gearing up for the former secretary of state.

“I think you’ll see a whole lot of people way outside the sphere of influence will be looking to get inside a sphere of influence,” said John Morgan, an Orlando lawyer and top party contributor.

Clinton spokesman Josh Schwer­in declined to comment on donor interest in a Biden run, saying in a statement, “Hillary Clinton is grateful to the hundreds of thousands of people who have stepped up to support her campaign and made her first quarter in the race a historic one.”

But the issue is expected to be a major topic when Clinton bundlers gather in New York next week for a meeting with campaign officials that was scheduled last month.

Biden’s potential candidacy has intrigued major party players who respect the steadfastness he has demonstrated as Obama’s vice president and admire what they describe as his down-to-earth decency. He has strong ties in particular to gay donors, who appreciate his early endorsement of same-sex marriage.

And many bundlers are pining to relive the frisson they experienced as players in Obama’s insurgent bid. After decades in Washington, Biden cannot claim to be an agent of change, but some donors consider him a continuation of the Obama era and its grass-roots appeal.

“There was energy around the genuineness of that campaign that I feel that we’re going to have with a Biden campaign,” said Shiva Sarram, an Obama fundraiser who has signed on to help the Draft Biden effort.

“I think there is a thirst for that genuine, honest candidate,” added Sarram, who runs a Connecticut foundation that supports war-affected children around the world. “That’s what Vice President Biden is to me: He’s trustworthy, he’s genuine, you know exactly what you’re getting with him, gaffes and all.”

Some top party fundraisers are also rattled by the news that the FBI is investigating whether Clinton’s use of a private e-mail server at the State Department put any classified information at risk.

“People are saying, ‘The press has always been out to get her, they are never going to let it go, she’s never going to get past it, what do I tell my friends?’ ” said one well-connected Democratic bundler. “It’s sort of the question of the moment.”

But Clinton campaign officials express confidence in the dedication of their supporters and shrug off the idea that some are having second thoughts.

“You can go around and find an anonymous donor to say something about anything,” campaign chairman John Podesta told reporters in Nevada on Monday, according to Politico. “But I think that we feel very good where we are.”

Many top Obama backers are strongly committed to Clinton, and said they will remain so even if Biden enters the race.

Andy Spahn, a major Hollywood fundraiser who advises film executive Jeffrey Katzenberg and director Steven Spielberg, wrote in an e-mail that he has “much respect for the job Joe Biden has done as VP but it’s too late in the game to mount a credible campaign. Hope he will join us all in support of Hillary Clinton’s candidacy.”

Gabriel Guerra-Mondragón, a former ambassador to Chile under Bill Clinton who is raising money for Hillary Clinton, said Biden does not have time to build a large war chest.

“It is too late to jump in,” he said.

Some senior Democratic fundraisers are skeptical that the 72-year-old vice president could mount the kind of operation needed to take on Clinton and then win the general election. “You’ve got to have a path,” said one top Obama bundler. “We had a plan in 2007 and executed that plan.”

Meanwhile, some Biden admirers who have signed up with Clinton feel torn.

“I don’t know that Biden can do it,” said a major fundraiser who has been fielding calls from other donors about the vice president. “It feels like another older white guy. Can he really pull it off? I’m really in a quandary.”

Biden supporters have begun pressing their case about how he could win. One of them is Joshua Alcorn, who was chief of staff to the vice president’s son Beau, who died of brain cancer in May, and now serves as senior adviser to the Draft Biden super PAC. He sent out a strategy memo Sunday to members of the Democratic National Committee, who are gathering for their summer meeting in Minneapolis this week.

“Since 2000, caucus and ­primary-goers have yet to coronate an inevitable nominee in the year before those contests take place,” Alcorn wrote.

One of his prime examples was mid-2007, when Clinton was still leading Obama in the polls.

Anne Gearan, Anu Narayanswamy and Karen Tumulty contributed to this report.