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.

Image A lot of Republican Party insiders think Jeb Bush could still be a serious presidential contender in 2012. Credit... M. Spencer Green/Associated Press

“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.

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.

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.