Advisers to President Obama are tiptoeing carefully around the political bounce he received after the successful raid on Osama bin Laden’s compound, wary of appearing unseemly, convinced the boost will be temporary and confident that the event will ultimately speak for itself.

But Obama is already stitching the victory into the broader tapestry of his 2012 reelection campaign. It fits neatly into one of his core messages, that Americans are capable of tackling in­trac­table, long-term problems. “Doing big things,” as he put it in his State of the Union address.

Before last Sunday night, Obama’s “big things” dealt mainly with reviving the sagging economy, investing in technology and infrastructure, and promoting energy independence. His examples of American resilience were anchored mostly in the past, as when he called last December for another “Sputnik moment” in demanding educational innovation.

Now, however, Obama has a new case study in American exceptionalism to invoke. And although White House advisers insist they are not incorporating the bin Laden raid into their political planning for 2012, they acknowledge it has the potential to do more than simply reshape his image as a decisive leader.

“If there’s an enduring impact of this, it will be a sense of what the president said in his State of the Union address,” Obama strategist David Axelrod said.

Like other top Obama advisers, Axelrod was careful not to paint the raid as a personal victory for the president. It “was not a political exercise, so I don’t want to treat it as such,” he said. At the same time, he said, there are “other challenges, and challenges people are facing in their daily lives, and those don’t go away simply because of this,” citing high gas prices and the economy, which could regain center stage as the excitement over the operation dies down.

“But it was a reaffirmation of that American determination and American spirit — the ability to do the things that some people thought impossible,” Axelrod said. “And that has value.”

Already, in several appearances since the raid, Obama has described it as a reminder that “as a nation there is nothing that we can’t do,” as he put it during an unrelated White House ceremony Monday. On Sunday night, during his first comments about the operation, he linked it to American values, saying the country is “once again reminded that America can do whatever we set our mind to.”

His most rousing remarks on bin Laden came Friday, before troops at Fort Campbell, Ky., where Obama not only hailed the bin Laden operation as a great American achievement but also tied it directly to the country’s ongoing economic woes, among other challenges.

“It’s easy to forget sometimes, especially in times of hardship, times of uncertainty — coming out of the worst recession since the Great Depression, we haven’t fully recovered from that, we’ve made enormous sacrifices in two wars — but the essence of America, the values that have defined us for more than 200 years, they don’t just endure,” Obama said, his volume rising.

“They are stronger than ever. We are still the America that does the hard things, that does the great things. We’re the nation that always dared to dream,” the president said. “We’re the nation that dared to take risks.” He cited the moon landing, D-Day and the civil rights movement, weaving together a story of the nation — and, without explicitly saying so, an argument for his presidency.

At least two public opinion polls show Obama’s popularity has risen since last weekend, but several Democrats argue that the event will not automatically carry Obama to reelection, or even sustain him through the summer. They point to false political turning points, big and small, in the past: former president George H.W. Bush’s defeat after winning the first Gulf War, and even the fleeting bounce Obama received in January after his heralded remarks on the Tucson shootings. At the same time, President George W. Bush won reelection in 2004 after failing to capture or kill bin Laden as he had promised after the 2001 terrorist attacks.

Democrats including Obama’s advisers said they expect the raid’s unequivocal success to put a stop to Republican arguments that the president is weak or indecisive — or constantly apologizing for the United States.

A senior administration official, who spoke on the condition of anonymity to speak freely about internal thinking, said the White House is not developing a strategy to leverage the raid in other difficult arenas, such as the budget or debt-ceiling negotiations with Republicans. And the official insisted it would not change the overall message or approach of the 2012 campaign, which has long been described as a campaign focused on the economy.

Still, it will almost certainly help a president elected on “hope” and “change” to shift his next campaign in a new direction. Even as Obama headed to Indiana on Friday to give an economic speech, White House press secretary Jay Carney said the tough political environment in the swing state was not a burden.

“I think that it’s a long time before next year’s election, and he’s focused on the things that a president needs to be focused on: our national security,” Carney told reporters aboard Air Force One. “His focus on that, I think, has been quite evident in the last several days, and the economy, which is what he’ll be focusing on today in Indiana. I think that the president firmly believes that making the right policy decisions tends to be beneficial come political season, but for him, at least, political season is a long way off.”