Mr. Obama has rewarded his top backers with coveted diplomatic posts like London and Tokyo, but he does not expend much personal energy when it comes to stroking donors: More than a dozen Obama supporters interviewed for this article described the president as an introvert who views big-dollar fund-raising as an unappealing, if necessary, chore. If the situation were a movie, one donor said, it would be titled: “He’s Just Not That Into You.”

Now, with political givers viewing the McAuliffe campaign as a way to curry favor should Hillary Rodham Clinton decide to run for president in 2016, the chatter among the donor class is about the striking contrast between the Obama and Clinton approaches.

“It’s a whole different shtick,” said Arthur L. Schechter, a Houston-based lawyer whose support for Mr. Clinton led to an ambassadorship in the Bahamas and who has also raised money for Mr. Obama. "The Clintons have a way of making people feel like they’re part of something and important to what’s going on, and I found that lacking in the Obama team," he added.

Several donors declined to speak for attribution because they did not want to anger the president. One called Mr. Obama’s White House holiday events “cuckoo clock parties,” because “he comes down, gives a speech, poses for some photos and pops back inside.”

David Plouffe, who served as Mr. Obama’s campaign manager in 2008, said the ethos of fund-raising started with Mr. Obama’s earliest donors in 2007. “It was about the campaign and the mission, not what they would get out of it,” he said. “That may be unusual, but it was a privilege to witness and it was successful.”