“Around the country they know me as George’s boy and George’s brother, right?” he said. “I’m proud of my family, but I’m not going to get elected by being the third Bush running for president. I got that. I’ve got enough self-awareness to know that that’s the case. I’ve got to go earn it.”

Some of Jeb Bush’s allies are keenly aware of the delicate balance required. Al Cardenas, a longtime Florida Republican Party leader and friend of his, said it was “never a ‘win’ situation” when Jeb Bush was asked about his family.

“Every time you have to face questions about your family’s performance, in some way it interrupts the journey of making sure that your own identity has clarity,” he said.

Jeb Bush has offered mild criticism of his brother’s administration at times. But it is not a role he seems to relish, as was demonstrated when he struggled over the summer to answer questions about whether he would have invaded Iraq, a decision that still weighs down the former president with many voters. The former Florida governor recognizes, however, that for political and symbolic purposes he must create space with his brother.

“My brother didn’t veto bills that he could have vetoed to send a signal that government needs to be reined in,” Mr. Bush said last week in New Hampshire. “Part of that related to the efforts to fight — you know, create the homeland security efforts and to fight the wars and all this. He needed the support to maintain that.”

Jeb Bush’s quandary is reminiscent of the one his brother faced in the 2000 Republican presidential primary. George Bush wanted to prove that he was his own man and, to conservatives, not a replica of his father, who increased taxes and faced a primary challenge from the right in his 1992 re-election bid. But then, as now, there was also considerable good will in Republican ranks toward the Bushes after eight years of having a Democrat in the White House.