On Thursday, Obama will attend the dedication of Bush's presidential library in Texas, a tableau that will draw attention to two distinct men a Republican and a Democrat from different ends of the political spectrum, political foils with polarized constituencies.
Indeed, Obama ran for president in 2008 as the anti-Bush, critical of the war against Iraq and of the economic policies of the preceding eight years.
But in his more than four years of governing, Obama has also adopted or let stand a series of Bush initiatives, illustrating how the policies of one administration can take hold and how the realities of governing often limit solutions.
Bush's signature education plan, No Child Left Behind, remains the law of the land, though the Obama administration has granted states waivers to give them flexibility in meeting performance targets. A Bush Medicare prescription drug plan, criticized for its cost, is now popular with beneficiaries, and Obama has sought to improve it by providing relief for seniors with high bills. Obama continued the unpopular bank bailouts and expanded the auto industry rescue that Bush initiated in 2008.
Bush authorized a military surge in Iraq in an effort to tame the conflict there. Obama completed the withdrawal of troops from Iraq but also authorized a military surge in Afghanistan before beginning a drawdown of troops that is expected to be completed at the end of 2014.
"The responsibilities of office drive presidents toward pragmatism," said Joshua Bolten, a former Bush chief of staff. Where those policies are effective, he added, "the successor has good reason to adopt them."
Obama, like Bush during his presidency, is seeking an overhaul of immigration laws that give 11 million immigrants in the U.S. illegally a chance to get on a path toward citizenship. Bush came up short in 2007, but Bolten believes that six years later the nation and its politicians are in a different place.
"President Bush was just ahead of his time and his party in recognizing both the importance of reaching some sort of bipartisan accommodation and on what the elements of that might reasonably be," he said.
Bruce Buchanan, a government professor at the University of Texas at Austin who specializes on the presidency, says it's not uncommon for presidents to hand off their agendas to another. Even measures or issues that were unpopular under one president can appear different with the passage of time and under the direction of a new occupant in the White House.
"While the names of the problems are the same, the stage of development is usually very different and the public stance of the president dealing with them is often very different," he said. "You have to be sensitive to those things lest you create the false impression that they are mirror images of one another, which I don't think would be accurate."
Even without the similarities, presidents are members of an elite club, one that gives them a unique appreciation for the travails they each face.
"Regardless of the times when they served and their political and policy differences, there is a commonality of experience that the president believes binds them together," White House spokesman Jay Carney said. "The responsibilities of the office are the same."
On no front are the similarities between the two presidents more striking than on counterterrorism. Obama did vow to end the harsh interrogation techniques such as waterboarding that had been employed during the Bush administration, and he issued an executive order upon becoming president declaring that the United States would not engage in torture.
But other practices continued and, in some case, expanded under Obama.
"The basic similarity is these are the only two presidents that have governed in a post-9/11 era, where the principal threat to the United States comes from terrorism," said Ben Rhodes, Obama's deputy national security adviser. "President Obama believes that we're at war with al-Qaida and its affiliated groups, has continued to take direct action against al-Qaida networks overseas and has continued to pursue very aggressive intelligence, law enforcement and homeland security measures that have been developed since 9/11."
Jack Goldsmith, who was an assistant attorney general in the Justice Department's Office of Legal Counsel during Bush's first term, says Obama's use of warrantless surveillance, military detentions without trial and increased drone strikes has received less pushback than it would under a Republican president.
Goldsmith, now a law professor at Harvard Law School, argued in a blog post after Obama's election that the public "generally trust the former constitutional law professor and civil liberties champion more than a Republican president to carry out these policies."
He added that "many on the left (in Congress and the NGO community, and perhaps the press) who might otherwise be uncomfortable with these policies will give President Obama a freer hand than they would a Republican president."
Still, Rhodes sees significant differences in Obama's national security approach.
Bush, Rhodes said, had defined the broad conflict as a war on terrorism and included Iraq as part of that war.
"We redefined the war as something more narrow, which was a war against al-Qaida and its affiliates, not against other states, not against nonaffiliated terrorist groups," Rhodes said.
Republican Sen. John McCain has a unique perch to assess both presidents. He ran against both in 2000 against Bush for the Republican nomination and in 2008 against Obama. He allied himself with both men on immigration and called on them to increase troop levels in Iraq and Afghanistan. An early opponent of waterboarding, he has applauded Obama's continued use of other counterterrorism measures.
"I think they both had an appreciation for the threat that we face," he said of the two presidents.
But he faults Obama for not leaving a residual force in Iraq and for creating uncertainty about what the U.S. presence will be in Afghanistan after 2014.
And he distinguishes between the presidents. Under Bush, he said the United States became a nation "that was ready to pursue our enemies."
"Obviously, President Obama viewed this as a time to withdraw and not to make military commitments overseas."
Rhodes makes a similar point, though differently.
"The trajectory under the previous administration was an increased military presence overseas," he said. "President Obama would like his legacy to be the reduction of military presence overseas and having, ideally, zero troops in harm's way."
Jeb Bush, Hillary Clinton on speakers' circuit
Dallas • Jeb Bush and Hillary Rodham Clinton are hitting the speakers' circuit on the eve of the opening of George W. Bush's new presidential library, stoking speculation about their own political futures. Bush, the former Florida governor, says in a speech to the World Affairs Council in Dallas that the nation needs to embrace changes to immigration and education. He says the issues are keys to growing the economy. Bush was joined by his son, George P. Bush, a candidate for Texas land commissioner. Asked about 2016, the younger Bush said with a smile he was focused on next year's land commissioner race. Clinton, the former secretary of state, was speaking Wednesday at a private event in suburban Dallas, her first paid speech since leaving the State Department. Though 2016 supporters rallied outside, Clinton offered no hints about her political future.