“George isn’t going to break that,” Mr. Bush said, meaning the ex-presidents’ code, “and if he was asked to serve in some way, he would do it, in spite of all the ‘it’s Bush’s fault.’ That’s just the kind of guy he is.”

Often depicted as the most mercurial and bookish of the Bushes, Jeb, who now runs his own consulting firm, seems at ease out of public office. He wore a loose-fitting guayabera, rather than a suit, and responded to questions amiably, with little hint of the prickliness that has sometime marked his interactions with reporters.

Mr. Bush said he met Mr. Obama in 2009 when he accompanied his father, George Bush, to the White House a few weeks after the inauguration. “He was extraordinarily kind and gentle to my dad, which I love,” Mr. Bush said.

He gives Mr. Obama credit for trying to spur innovation in public schools, a policy area about which Mr. Bush is passionate, but his admiration ends there.

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“By and large, I think the president, instead of being a 21st-century leader, is Hubert Humphrey on steroids,” Mr. Bush said. “I don’t think there’s much newness in spending more money as the solution to every problem.”

Though he headlines the occasional fund-raiser around the country, Mr. Bush has exercized his political influence this year largely out of the public view. He has been deeply involved as an informal adviser to the party’s candidates for governor, whom he sees as the most likely sources of new Republican policy ideas. “It doesn’t seem like it’s going to be happening in Washington anytime soon,” Mr. Bush dryly observed.

No matter what happens in November’s midterm elections, Republicans will have to make a difficult calibration as they head into the presidential season. The party needs a messenger who can keep its Tea Party-type activists energized behind an agenda and a nominee. But Republicans will also be looking for someone who can reposition the party nationally and make its more strident ideology palatable to the wider American electorate.

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This explains why some influential Republicans persist in believing that Mr. Bush might still make a strong candidate in 2012. He is a favorite of the anti-establishment crowd (he is said to have mentored Marco Rubio, the Senate challenger in Florida who gave the Tea Partiers a national lift), but he is also a political celebrity with a pronounced independent streak. As governor, for instance, Mr. Bush strongly opposed drilling in the shallow waters off Florida, and he favors increasing legal immigration, rather than restricting it.

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Mr. Bush says he has no interest in running, because he wants to make money for his family, but his political allies seem to read a “for now” into such statements. “Every presidential wanna-be and every member of the House and Senate I talk to, if you ask them who is a difference-maker in our party, they will tell you Jeb Bush,” said Al Cardenas, the former party chairman in Florida.

Washington wisdom — such as it is — holds that the real impediment to Mr. Bush’s political future would be the Bush brand, which has taken a pounding both inside the party and out. Neither George W. Bush nor his father ranks among the more successful presidents of our time, to put it politely.

Jeb Bush’s admirers insist, however, that whatever cloud existed over the name is lifting, as memories of the last Bush era recede, replaced by a hardened conservative opposition to Mr. Obama’s policies. And those who know Mr. Bush say he has never concerned himself with it. “He’s the guy who cares about that the least,” said Nicholas Ayers, executive director of the Republican Governors Association.

In fact, talking to Mr. Bush, one senses that the problem for him as a future candidate might not be the efficacy of the Bush brand, but rather what he might need to do in order to transcend it. George W. Bush ran successfully for president in part by putting some distance between himself and his father, signaling to the Republican base that he was more a Reagan conservative than he was a “read my lips” pragmatist.

It is harder to imagine Jeb Bush, the fierce defender of his family, ever publicly acknowledging his brother’s failures in a way that would enable him to come across as a different, more capable kind of Bush. When I asked him whether Mr. Obama had a legitimate point — whether his brother’s administration did, in fact, bear responsibility for the country’s economic collapse — Mr. Bush paused and, for the only time in our interview, appeared to carefully assemble his words.

“Look, I think there was a whole series of decisions made over a long period of time, the cumulative effect of which created the financial meltdown that has created the hardship that we’re facing,” he said slowly. “Congress, the administration, everyone can accept some responsibility.”

“The issue to me is what we do now,” Jeb Bush said. “Who cares who’s to blame?”