The Obama’ team’s PowerPoint presentation, which has also been shown to donors in Austin, Dallas, New York, Los Angeles, San Francisco and Boston, presents donors with polling that shows Mr. Romney and former Arkansas Gov. Mike Huckabee running 5 percentage points behind Mr. Obama, while Newt Gingrich, Sarah Palin and Michele Bachmann trail by double digits. Mr. Messina, according to donors in Florida, said last week he wouldn’t be surprised if Ms. Bachmann, who raised $13 million for a congressional election last fall, wins the Iowa caucuses.

Sean Spicer, communications director at the Republican National Committee, said the president’s political allies must realize they’re in a tough spot if they’re highlighting how he matches up against potential rivals and not simply focusing on Mr. Obama’s record in office.

“So the president’s big case is: I’m up by a few points among people with a lot less name recognition at a time when the public is not fully engaged in the race?” Mr. Spicer said. “That’s not a real compelling argument.”