Barack Obama flew to Fort Campbell on the Kentucky-Tennessee border on Friday to thank in person the assault team who stormed Osama bin Laden's hideout. He has good reason to do so: the raid has transformed the way Americans view their president, changing him overnight from dithering nerd-in-chief to decisive action man.

At emotional meetings, held behind closed doors to protect their anonymity, he awarded the units involved the highest honours available to him and heard their first-hand accounts of what happened inside the Abbottabad compound.

Afterwards, at an open meeting at the base with other troops, there were cheers when Obama spoke of these "quiet professionals" who had ensured that the terrorist behind the 9/11 attacks "will never threaten America again". He had told them: "Job well done."

The president spoke to a hangar full of cheering soldiers after meeting privately with the full assault team, army helicopter pilots and navy seal commandos who executed the dangerous raid on Bin Laden's compound and killed the al-Qaida leader in Pakistan early on Monday.

"Thanks to the incredible skill and courage of countless individuals … the terrorist leader that struck our nation on 9/11 will never threaten America again," Obama said, speaking at an army post whose troops have sustained heavy losses in a war in Afghanistan, losses that have grown on his watch.

A US official said that material retrieved from Bin Laden's compound shows he was in touch with senior al-Qaida figures and was able to plot future attacks on US targets from his suburban Pakistani hideout. The official said the trove of documents and computer material also includes new video of Bin Laden, both unreleased propaganda tapes and more candid shots like home videos.

Obama owes a large debt to the special forces. Since he began campaigning for the presidency in 2007, he has faced criticism that he was not up to the job. First, the Hillary Clinton campaign implied that he was too inexperienced, that he could not handle the 3am crisis call. More followed from John McCain and Sarah Palin. Then came the rightwing commentators Rush Limbaugh and Glenn Beck and the Tea Party movement. He was too detached, too academic. His patriotism was questioned as was his religion.

Stephen Hess, one of America's most respected commentators on the White House, acknowledged Obama's changed status since the death of Bin Laden. "His image, fair or unfair, is that he is an intellectual, which he is and which is unusual in a president. Obama thinks about things and takes his time in making decisions, which I think is a good thing."

But Hess, a political scientist at the Brookings Institution, saw the Abbottabad decision as "gutsy, tough, made quickly" and responsible for changing the dynamics of American politics. "It is going to be very hard for Republicans to use any more that label of weak and indecisive," he said.

Helping to reshape the image are those pictures of Obama in the situation room looking grave, grim and anxious as the raid is taking place. He was risking not only the special forces he had sent in but his own presidency, with the danger of a Jimmy Carter-style Iranian hostage rescue debacle that could have finished any hopes of a second White House term.

Richard Wolffe, the author of two books on Obama, acknowledged that the perception had changed but insisted the view of the president as weak and naive was always wrong. "If he was as cautious as people said, he could have flattened the building with a bombing raid," he said.

"He makes a few big gambles, but cautiously. He will make the gutsy move, but gets there more slowly. It is a weird combination because we are used to someone who shoots from the hip like Bush or someone more hesitant like Kerry or Clinton. But we have someone who is a combination of the two, someone who is cautious but who makes the calls." There is a hard core that will never be convinced that Obama is truly patriotic and will continue to insist he was not born in the US, that he is a secret Muslim. But their numbers have dwindled fast because of the combination of his release of his birth certificate a fortnight ago (and his ridiculing of Donald Trump at the White House correspondents' dinner) and the Abbottabad raid. Beck, Limbaugh and former members of the Bush administration joined in the praise.

David Frum, who as an assistant to Bush wrote the "axis of evil" speech, deplored the vilification of Obama as some dark-skinned alien. "So we had this situation where he was not an American, a Muslim, not a patriot. I do not think it [the Bin Laden killing] ends the paranoia but it shoves it back from the centre to the margins. He has shown he understands that the nation has enemies and that force is sometimes the only remedy," Frum said.

The White House and Pentagon almost threw away their advantage with its poor handling of the aftermath, offering exaggerated accounts of what happened and then having to recant. Obama's meeting with the 9/11 relatives on Thursday and his trip to see the troops at Fort Campbell have undone some of that damage.

Within minutes of Obama announcing last Sunday that Bin Laden was dead, US commentators were tweeting that the president had the 2012 election in the bag. That is grossly premature. Obama has not enjoyed the kind of spectacular jump in approval ratings that he might have expected. He has not soared into the 80s, instead seeing relatively modest rises that take him from the mid-40s to the mid-50s. That is mainly because of the sluggish economy.

Democratic strategists, speaking anonymously, reluctant to sound negative in a week of good news for the president, are far from convinced he is invincible and are nervous about the slowness of the economic turnaround.

Brad Coker, managing director of Mason-Dixon polling, agrees. "There is no reason for Democrats to say it is over. I think Republicans thought the same thing in 1991." George Bush Sr had seen the Berlin Wall fall on his watch and had high approval ratings for his handling of the Gulf war, but still lost.

"There is plenty of time for Obama's shine to fade. Now you have all this stuff surrounding the release of these photos. Not wanting to put them out feeds into the old Obama image, not wanting to offend Muslims. We are a tabloid country. We want to see pictures of Bin Laden," Coker said, predicting that Obama's modest boost in the polls would last only a week before being halved.

Obama came to power with some of the highest approval ratings in US political history. Millions turned out for his victory night party and inauguration. He has managed to get some of his programme through, delivering on his promise to introduce near-universal healthcare, due to begin in 2014. He has had other gains too, on gay rights, a US-Russian arms reduction deal and preventing the shutdown of government. But there is a lot left to do, including closing Guantánamo, reforming immigration laws and ending tax breaks for the wealthy. These failures have brought criticism from the left. Clarence Jones, a former lawyer and adviser to Martin Luther King, writes regular commentaries calling on the left to mobilise and press Obama to do more. While pleased that it went well in Abbottabad, he would like to see the president "apply the same careful, premeditated, calculating weighing of options about major domestic issues as he did in determining which course of action to pursue to get Bin Laden". Jones, who helped draft King's "I have a dream" speech, believes there was an undercurrent of racism behind many of the jibes about the president not being up to the job. "Yes, his academic professorial background was used by his critics to portray Obama as some ivory tower intellectual incapable of taking decisive action. Regrettably there was a racial undercurrent in the suggestions he was not up to the job." Jones does not believe that the removal of Bin Laden has exorcised that.

Politics will return to normal in Washington next week. The Republicans will resume their confrontation with the White House over the size of the national debt. Catching Bin Laden has given Obama an edge in those negotiations and an edge in the longer term. National security is usually a point of weakness for Democrats. But next year, if any Republican rival questions his credentials, the president will have an easy, one-word answer: "Osama".