“The smart money is taking it slower and waiting to see who runs and how these candidates develop a platform,” said Scott Reed, the top political adviser to the U.S. Chamber of Commerce. “Raising money is an important part of the game. But it’s not the whole game.”

The first primary votes are still nearly 10 months away, giving Mr. Bush’s team plenty of time to adjust, and Republicans show no sign of unifying behind another candidate. Mr. Bush’s advisers say he never believed he would be able to clear the field. And they say his refusal to bend to the demands of people whose views he does not share demonstrates that he is running a different type of race.

“As Governor Bush considers the possibility of a run, he’s working hard to earn the support of people throughout the party and deliver a positive message about how conservative reforms can restore opportunity and prosperity for more Americans,” Kristy Campbell, a spokeswoman for Mr. Bush, said in an email.

In January, Mr. Bush’s allies started using the phrase “shock and awe” to describe his plan to lock up as many of the party’s major donors and policy experts as possible. The intent was to make him the sole credible contender for the blessing of the Republican establishment. Mr. Bush was successful in driving the 2012 nominee, Mitt Romney, from trying another campaign. And few doubt that he leads in fund-raising, though his organization will not have to disclose its finances until July.

But while Mr. Bush continues to position himself as Republicans’ best hope in the general election, recent polls show him performing no better against Hillary Rodham Clinton than Gov. Scott Walker of Wisconsin or Senator Rand Paul of Kentucky. And he is well behind Mr. Walker in Iowa, which has made a habit of rejecting candidates seen as their party’s inevitable nominees.

“If he’s going to run for the presidency because his father and his brother were president, is that why we should support him?” asked Colleen Platt, a City Council member in University Park, Iowa.

There is also lingering suspicion of Mr. Bush among the Tea Party grass roots, which arose while Mr. Bush was focused on business and philanthropic interests.