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.

For decades, the Bushes were a dominant clan of the Republican party, starting in the 1980s when patriarch George H.W. Bush became vice president, then president. But the family fell out of favor with the American public as well as with a chunk of the Republican Party in the waning years of his son's wartime presidency, and George W. Bush was deeply unpopular in its aftermath. But that's started to change; a Gallup Poll last month showed nearly half of Americans now view him favorably, a post-presidential high.

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 Republican official and government professor at Claremont McKenna College in California. "They are playing the long game. They are looking ahead."

Indeed, George P. Bush, who is running for Texas land commissioner, is convening a conference in Miami this weekend in the nation's largest swing-voting state. His father and other Republican luminaries will address young leaders.

These days, the family's presence is most felt in the debate on immigration, an issue that could affect the Bushes' future political prospects as well as their party's. While the conservatives who dominate the party oppose an eventual pathway to citizenship for the estimated 11 million immigrants now in the country illegally, the Bushes are pushing what they see as pragmatism. They argue that such a measure would boost the country's economy and help the Republicans, which has struggled to attract Hispanic voters.

On Wednesday, George W. Bush made a rare post-presidential foray into the political arena, using his brief remarks at a naturalization ceremony in Dallas to urge Congress to fix a "broken" immigration system and reach a "positive resolution" on reform legislation. In recent months, Jeb Bush has been making the rounds with conservative groups, urging Republicans to shed the perception that they're "anti-everything" and embrace an immigration overhaul.

"I'm here to tell you there is no 'us' or 'them,'" the former Florida governor told activists at the Conservative Political Action Conference in Washington. "The face of the Republican Party needs to be the face of every American, and we need to be the party of inclusion and acceptance."

He is likely to make a similar pitch at his son's conference this weekend in Miami. He'll share a speaking card with Sen. Marco Rubio, one of the leading authors of the broad immigration bill that was approved by the Senate but faces strong opposition from House conservatives.

Friends and advisers say the advocacy is personal for the Bushes, who have long been pained by the growing divide between many Republicans and Hispanics.

George W. Bush tried and failed to pass immigration legislation during his presidency, blocked by conservatives in his own party who dismissed it as "amnesty" for lawbreakers. He has said it was one of the biggest disappointments of his administration, confiding to some that he regrets not pushing for reform in his first term, said Al Cardenas, chairman of the American Conservative Union and a longtime Bush family friend.

Jeb Bush has long championed the immigration cause. His wife, Columba, is of Mexican heritage. The two met while Bush was an exchange student.

Both brothers were governors of states with large Hispanic populations that they had to court to achieve political success.

Still, many say the Bush appeals will do little to sway a new generation of conservative Republicans who came to power after George W. Bush left the White House. His administration's deficit spending and its bailout of the big banks fueled the rise of the anti-government conservative activists, which helped elect a crop of no-compromise lawmakers.

Nevertheless, Ana Navarro, a strategist who led Hispanic outreach for Sen. John McCain's presidential campaign, said the Bushes bring political credibility to the immigration debate, particularly for Republicans eager to win national elections.

Mitt Romney won just 27 percent of Hispanics' votes in last year's election.

The Bushes, Navarro said, "remind Republicans that once upon a time, not too long ago, there was a Republican presidential candidate who got 44 percent of the Hispanic vote."

Regardless of the immigration outcome in Washington, the biggest political beneficiaries of the Bushes' public push could be the Bushes themselves.

Jeb Bush may run for president in 2016, and his son, George P., a 37-year-old Spanish-speaking attorney and consultant, is attempting to launch a political career of his own in Texas.

The push can have other benefits for the family as well, particularly as George W. Bush — who re-emerged in a public way in April with the opening of his presidential library — tries to define his legacy.

While his approval ratings are rising, the Gallup Poll last month found that 69 percent of Americans feel the former president bears a great deal or a moderate amount of the blame for the country's current economic problems. A survey last year found that just 25 percent thought Bush's presidency would be viewed by history as "outstanding" or "above average."

In a series of recent interviews with network news channels, he has emphasized his work fighting AIDS in Africa. This week, after his remarks at the Dallas naturalization ceremony, Bush's presidential center held panel discussions on another topic: immigration.