“A presidential library is you forever, and I’m not talking about the president, I’m talking about the staffer,” said James L. Rutherford, the dean of the Clinton School of Public Service, who played an influential role in the creation of the Clinton library in Little Rock, Ark. “It’s not a just a presidential legacy, it’s a place for your time and your experience in that administration.”

The White House disputed any internal tension and insisted that Ms. Jarrett and everyone else are focused entirely on the pressing issues of the day. “This is a project that isn’t even at its inception yet,” a White House spokesman, Eric Schultz, wrote in an email. “The priority of everyone at the White House is to focus on achieving the president’s second-term priorities over the next three years.”

But at least some small sliver of bandwidth is concerned with the library foundation, and paying for it.

Fund-raising for a post-presidential project is a slog even for politicians like Mr. Clinton who enjoy schmoozing donors. Over the years it has become clear that for Mr. Obama, stroking wealthy contributors is a loathsome activity. But it is a necessary one for his last act, and there are signs the Obama money machine is starting to stir.

Ms. Mastromonaco has welcomed top Obama fund-raisers into her West Wing office to discuss the technology that could distinguish the library and the potential issues that could serve as a suitable mission for Mr. Obama’s post-presidential years, according to one such visitor. Mr. Nesbitt, who has a private equity firm, met this spring with Marc Lasry, a hedge fund billionaire in New York, and told him that the president “was thinking about” the post-presidency, Mr. Lasry said. And Ms. Smoot has begun making the rounds.

“Julianna has been talking about this for more than a year,” said one Obama bundler in Chicago, who called himself “likely to be involved.”

Previous campaign supporters who have recently met with Mr. Obama said he had in no way solicited contributions. But they also noted that he has increased his outreach. The president has shown more “good will” to the business community, said Tony James, president of the Blackstone Group, who met with him in the Oval Office in August. Chicago financiers have also appeared recently on Mr. Obama’s radar.