When the history of the Obama presidency is finally written, the killing of Osama bin Laden will stand as one of the seminal moments and greatest accomplishments. What it may mean for President Obama’s 2012 reelection campaign and for the Republicans challenging him is more difficult to measure.

The reasons have little to do with the significance of what happened Sunday or Obama’s role in ordering a genuinely risky but ultimately successful mission to take out the most notorious terrorist in the world, the man responsible for the attacks on Sept. 11, 2001.

Instead, the reasons have much to do with issues that have been and remain paramount in the minds of Americans: jobs, the economy, debt and deficits. As James Thurber, a political science professor at American University, put it in an e-mail message Monday, “Jobs and the performance of the economy are still and will be the primary factors influencing 2012.”

That means other questions become crucial in assessing the longer-term implications of the death of bin Laden for Obama’s presidency. One is whether this week will be seen as a moment that marked a genuine and lasting turnaround for the president after ups and downs since last November’s midterm election shellacking.

Another is whether Obama and his advisers can find a way to translate the elements that contributed to Sunday’s success into a broader narrative: one that connects the elements that made the mission successful to their efforts to revitalize the economy and deal with other pressing domestic problems. Will the killing of bin Laden improve the public’s gloomy perceptions about the direction of the country?

Obama and the intelligence and military forces that carried out the mission are being widely and justly praised across the political spectrum for bringing bin Laden to justice. But just as feelings of national unity surrounding Sept. 11 dissipated over time, so to is this likely to fade in its political significance, according to both Democrats and Republicans.

After his midterm setback, the president saw a brief rise in his standing after his January speech at the service for the victims of the shooting in Tucson. But in the most recent round of polls, Obama’s approval rating had slid once again to some of the lowest of his presidency.

The boost now could be even more significant, given the historic importance of the death of bin Laden and the emotional strains from Sept. 11 that remain just below the surface of American life. Republican pollster Bill McInturff said his analysis of the impact of major foreign policy successes in previous administrations points to a rise in Obama’s approval rating of about 13 percentage points that could last four to five months before beginning to reverse.

When Obama ran for president in 2008, his rivals questioned whether he had the experience or the resolve to be an effective commander-in-chief. Those questions persisted into his presidency, which is why the cost of failure in Pakistan Sunday would have been enormous, as former president Jimmy Carter learned after the failed mission to rescue U.S. hostages in Iran during his presidency.

Republican candidates have regularly questioned Obama’s foreign policy prowess, most lately his response to the popular uprisings in Egypt, Libya, Syria and elsewhere in the Middle East, where they have called him tentative and passive in exercising U.S. leadership. That could continue, though even GOP strategists believe they will now have more trouble challenging Obama on his handling of the war on terror.

“This probably answers the toughness argument about the commander-in-chief because it [the mission] wasn’t a sure thing,” said Rudy de Leon, a former deputy Defense secretary in the Clinton administration, adding, “It was a tough decision and it was not a passive decision.”

Democratic pollster Peter Hart said that beyond the issue of toughness, Obama on Sunday night was able to speak to the overall mood of a country that has been through tough times. That could help turn this event into a broader boost for his political standing.

“You looked at him last night [Sunday] and said this is somebody who had a steel backbone and a sense that he had a real understanding of the moment— no sense of celebration,” Hart said. “He caught what I thought was the tenor of the times — a country that has been down and that there is a way of coming back.”

Republicans and Democrats agreed, however, that economic issues would play a far more influential role in the next election than this episode. “I don’t think in any way, shape or form the election will be about this,” said Democratic pollster Mark Penn, who as Hillary Rodham Clinton’s chief strategist in 2008 was responsible for a pointed television commercial questioning Obama’s national security credentials.

He added: “But at issue has been his leadership, his engagement in some areas. He’s shown extremely strong leadership here in doing something I think the American public wanted done. . . If he can build some momentum and confidence around his leadership, starting here, I think this could be a point to look back upon and say, “Ah ha, that was the point he found surer footing.’”

Scott Reed, a Republican strategist, called the killing of bin Laden a big victory for the president and the country. “But the country here is still hurting, with no jobs and gas prices and no hope when it comes to economic growth,” he said. “So while it’s a huge, huge victory and they all should be commended for how they executed it, he still has some serious domestic issues in front of him and they can’t be understated.”

The killing of bin Laden produced varying reactions from Obama’s prospective 2012 rivals. Some congratulated the president by name. Others were less effusive about Obama, and some did not even mention him — a mistake, according to some GOP strategists.

“I think you respond like an American and you praise the president and the troops and special forces for a job extremely well done,” said pollster Whit Ayres, who has signed on to work for former Utah governor and U.S. ambassador to China Jon Huntsman Jr., who will soon decide whether to run in 2012.

“The best way for Republicans to deal with this is the gold watch strategy,” said GOP strategist Alex Castellanos. “Say, ‘Thank you, Mr. President, that’s great. Now about the economy?’ ”

Obama and his advisers certainly know that. The president has achieved a victory that has been at the top of the national security priority list since Sept. 11. He will be judged in 2012 in part on that success—but only in part. Voters will want to see success at home before they make their final decision.