THE THIRD WAY/THE BUSH WAY:

This week, former President George W. Bush surfaced from a self-imposed political exile to prod reluctant Republicans toward a broad immigration overhaul. He's also talking up his work on AIDS and cancer in Africa.

His brother, former Florida Gov. Jeb Bush, has written a book on immigration reform and is keeping the door open to his own presidential run in 2016.

And George P. Bush, Jeb's oldest son, is running for statewide office in Texas. [...]

With their image on the rebound, family members are openly criticizing their own party and promoting a more moderate -- they would say inclusive -- brand of Republicanism, one that could lay the groundwork for the next generation of a Bush dynasty.

"They are trying to redefine the mainstream," says Jack Pitney, a former national GOP official and government professor at Claremont McKenna College in California. "They are playing the long game. They are looking ahead."

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