He does not speak on the stump or appear in television ads. Campaign audiences rarely hear his name.

But aside from President Barack Obama and Mitt Romney, no one has shaped the 2012 election more than George W. Bush — on the economy and on the foreign policy issues in the spotlight during the final presidential debate on Monday.

For Romney, the battered reputation of Bush, the last Republican president, represents a burden to minimize in a tight race for the White House. The two have not appeared together this year.

When an audience member asked about Bush in the debate last week, Romney separated himself from what he characterized as Bush’s shortcomings on the budget deficit and on trade with China.

For Obama, Bush’s economic record offers a shield against voters’ wrath over high unemployment and slow growth; majorities in polls describe the nation’s economic woes as something the incumbent inherited rather than caused.

Obama benefits, too, from Americans’ weariness with the long wars in Iraq and Afghanistan, which Bush initiated. By winding them down — and by succeeding where Bush failed in hunting down Osama bin Laden — Obama has lately won higher marks from voters on foreign policy than on his job performance overall.

Both the president and Romney tried to use Bush to their advantage in Monday night’s debate. Obama said his opponent had “praised George Bush as a good economic steward and Dick Cheney as somebody who shows great wisdom and judgment.” But it was their strategies, the president suggested, that “got us into this mess.”

Romney, referring to the government’s bailout of the auto industry, said Bush “wrote the first checks.” Romney said he disagreed with that and would have preferred a “managed bankruptcy” instead.

The whole situation has become an awkward one for Bush loyalists active in the Republican campaign this year, one they like to avoid.

“I have no interest in participating in this silly exercise,” Karl Rove, a former Bush strategist who now leads Republican super-PAC efforts to aid Romney, said in declining to be interviewed about Bush’s influence on this election. He left it to Democrats to assess his former boss’ impact, and they were more willing to take the bait.

“There’s no question that George Bush tarnished the Republican brand nationally on both national security and the economy,” said Mark Mellman, a pollster for many Democratic candidates, including John Kerry, Bush’s opponent in 2004. “Republicans are living with that problem.”

Less than four years after Bush left the White House, the problem is at once pervasive and inconspicuous — as the former president has been since he left the White House. As he put it in a rare interview this summer, “I crawled out of the swamp” of Washington.

“He hardly ever comes up in focus groups,” said a top campaign adviser for Bush who asked not to be named. When voters think about the Republican Party’s identity today, they are more likely to point toward the tea party movement.

But because of Bush, the adviser added, voters give Obama “a great deal of slack” in assigning responsibility for the weak economy.

Democratic strategists echo the point.

“I just don’t see how Obama could have survived these economic conditions without that history,” said Stan Greenberg, a Democratic pollster and a former adviser to Bill Clinton.

Obama casts Romney’s policies as like Bush’s but as even further to the right, on taxes, regulation and a predilection for military confrontation with other countries. He generally does not mention Bush’s name, to avoid the appearance of trying too hard to pass blame to his predecessor.

“The issue isn’t to relitigate the Bush years,” said David Axelrod, the president’s political strategist. “It’s to make the case that we shouldn’t relive them.”

Romney has the tricky task of trying to mobilize the same conservative Republicans who backed Bush while casting his policies as a departure. With Democrats charging that his economic plan is like Bush’s tax cuts of 2001 and 2003 “on steroids,” Romney says his tax proposal is “not like anything that’s been tried before,” because it couples rate reductions with the elimination of some deductions.

“President Bush and I are different people, and these are different times,” Romney said in the debate last week. On trade, he said: “I’ll crack down on China. President Bush didn’t.” On the deficit, he said: “I’m going to get us to a balanced budget. President Bush didn’t.”

Neil Newhouse, Romney’s pollster, said, “We’re running a campaign for the future.”

Separating himself from unpopular aspects of Bush’s interventionist national security posture can prove complicated for Romney, who lacks foreign policy experience. Advised by some veterans of the Bush administration, Romney uses muscular language while depicting Obama as weak in projecting the United States’ leadership.

Yet he embraces Obama’s plan to end the war in Afghanistan by removing troops in 2014.

For now, at least, that stance reflects the Bush administration’s legacy on U.S. opinion.

“Whoever’s elected is going to have to live with the reality of what you might call intervention fatigue,” said Richard N. Haass, a State Department aide under Bush who now serves as the president of the Council on Foreign Relations. “There’s a real sense that our military interventions have not produced results that are in any way commensurate with their human and economic costs.”

Bush’s former aides chafe at criticism of his record from fellow Republicans, as well as from Democrats. Tony Fratto, a spokesman in the Bush White House and the Treasury Department, rebutted both of Romney’s barbs from the debate last week.

“There are good reasons why we didn’t balance the budget,” like the war on terrorism, Fratto said. On trade, “we were very effective with the Chinese” in paving the way for a rise in the value of its currency, to the benefit of U.S. businesses.

But like his former boss, who has offered only a cursory endorsement of Romney, he prefers not to say too much.

“I take my lead from President Bush,” said Fratto, who is now a partner in the consulting firm Hamilton Place Strategies. “He’s not interested in making it more difficult for the Republican nominee to get elected.

“We’ll work with the historians, and let candidates be candidates.”

© 2012 The New York Times Company