Some say it was the bullet to Osama bin Laden's head. Others point to the Republicans' seemingly insatiable desire to inflict self-harm since they took back control of the lower house of Congress in last year's elections. And then there is the growing realisation that Barack Obama might just have saved America from economic disaster.

Whatever the cause, a president who just a few weeks ago was regarded by his political opponents as being on the ropes before the fight for re-election had even properly begun is now being treated with a new, grudging respect as his poll numbers rise and he comes out punching.

Earlier this year, even those who argued that Obama was still favourite for re-election in 18 months were forced to concede that he was being dragged down by a host of problems.

His popularity ratings plummeted as many independent voters shied away from a president they regarded as too ideological on issues such as healthcare reform and not focused enough on economic revival or cutting the deficit. The drumbeat of rightwing radio and Fox News constantly questioned the president's legitimacy and painted him as somehow un-American. Even among many of Obama's supporters there was disillusionment at what they saw as his disinclination to stand up for what he, and they, believed in. He was too cowed by criticism from the right, they said; too willing to seek a consensus that amounted to surrender.

In November, the Republicans seized control of the House of Representatives, greatly reduced the Democratic party's majority in the Senate, and declared the victory as a repudiation of all that Obama stood for. It was a stunning reversal for a man who had won an election just two years earlier with a message of hope that seemed to have buried a disheartened and divided Republican party.

But in recent weeks Obama's approval ratings have risen significantly – to a 16-month high of 53% in the most recent poll – and the president is widely thought to have rediscovered some of his old political mojo in the wake of the raid to kill Bin Laden.

The death of the al-Qaida leader cut the ground from under the rightwing pundits and their constant refrain that Obama is weak and endangering America. Even George W Bush's defence secretary and vice-president, Donald Rumsfeld and Dick Cheney, grudgingly praised the president. Since then, the ideological fissure within the Republican party over budget cuts has been laid bare, leading it to make the colossal misstep of proposing to privatise medical insurance for the elderly, alienating much of the baby boomer generation. The party paid the price last week in an upset win for the Democrats in a New York state congressional election.

Meanwhile, Obama's crowd-pleasing tour of Ireland and Britain did him no harm back home.

For many pundits, that recent run of success was making the president look like a certainty for re-election. But then on Thursday, the well was poisoned by a single statistic: that US economic growth had slumped to an annualised rate of just 1.8% in the first quarter of this year.

"That's miserable," said Larry Sabato, head of the University of Virginia's Centre for Politics, who has made a speciality of studying the factors that influence presidential elections. "There's probably only one thing that can beat Obama. You never know about scandal, but I doubt it. War and peace: we don't have Iraq now and Afghanistan's winding down. But the economy – I don't care how good a president he looks a year and a half out, if you have a growth rate that is well below 3%, that president is probably going to lose as long as the opposition party nominates a respectable candidate."

That's a big "if" for the Republican party as it kicks off more than a year of wrangling between its political head and ideological heart to find a champion.

Obama has most to fear from a moderate Republican candidate. Three stand out among those likely to run: Mitt Romney, the former Massachusetts governor; Tim Pawlenty, the former Minnesota governor, and Jon Huntsman, the former US ambassador to China and ex-governor of Utah. All are former state governors, who often make compelling candidates – think of Bill Clinton, a former governor of Arkansas – because they are used to winning and using power by reaching across the political divide.

On paper, Obama should be most worried about Huntsman – but only for the reasons that make it likely that Huntsman's own party will reject him.

An anti-Huntsman spoof campaign advert produced by conservative bloggers shows images of a rhinoceros pounding through the African bush. No subtlety there: conservative critics of moderate members of their own party deride them as Rinos – Republican In Name Only.

The advert highlights Huntsman's criticism of the divisiveness of American politics ("Yelling and screaming and finger pointing. We all want the same thing"), the need to regulate carbon emissions, his assertion that "healthcare is a right" and, perhaps most contentious of all, his support for Obama's economic stimulus policies.

Close to the end, the video shows Huntsman endorsing John McCain – something of a hate figure on the right these days – in his 2008 presidential bid. The video closes by saying: "Not authorised or endorsed by Jon Huntsman or anyone affiliated with his campaign. Obviously."

Huntsman's position on almost all the issues for which he is targeted in the video would give him cross-party appeal in a head-to-head with Obama, drawing in many independents and conservative Democrats disillusioned with the president. But his problem will be to attract support in primaries where Tea Partiers and libertarians, who are deeply hostile to government in general and who loathe Obama in particular, will reject Huntsman not least because he has in the past praised the president.

"The Republican base hates Obama so much that one would think they would nominate a candidate who can beat him even if that person isn't perfect in their minds," said Sabato. "But you can argue it another way. You can say they hate Obama so much that they will nominate the candidate who hates Obama as much as they do."

In a Gallup poll released on Thursday, Huntsman fared the worst of the three Republican contenders thought most likely to be able to bring down Obama. He pulled in just 2% of support among likely Republican primary voters. Romney leads the field with 17%; Sarah Palin sits just a couple of points behind.

Romney has moved further to the right as his aspirations have grown but he has enough crossover appeal to be palatable to many independents. Tea Partiers and small-government activists, however, do not like it that, as governor, he signed legislation that provided near-universal healthcare insurance for Massachusetts residents – not least because health reform is now a favourite conservative stick with which to beat Obama.

But if the Republican right can forgive Romney such ideological transgressions, those same issues could prove powerful in luring the independents and conservative Democrat voters who are unhappy with Obama's first term.

Not so with Palin. After months of debate over whether she would or would not run, the charismatic but divisive 2008 vice-presidential nominee took a major step toward launching a presidential bid this weekend with the start of her "One Nation" bus tour of America's east coast, which has all the hallmarks – including the red, white and blue bunting on the bus – of an old fashioned whistlestop campaign tour.

Palin's recent purchase of a house in Arizona and the recruiting of an expanded staff has intensified speculation that she is about to enter the race.

Her star has fallen considerably since it shone so brightly over the Republican landscape three years ago. Some of her erstwhile supporters have grown weary of her political missteps, such as her ill-judged defence of gun-toting rhetoric after the shooting of Arizona congresswoman Gabrielle Giffords in January.

Others have been driven away by Palin's vague blandishments when it comes to policy specifics on issues that matter to them – concerns that will have been reinforced by the hokey statement she put out about her bus tour: "Our nation is at a critical turning point. As we look to the future, we are propelled by America's past," she wrote. "It's imperative that we connect with our founders, our patriots, our challenges and victories to clearly see our way forward. A good way to do this is to appreciate the significance of our nation's historic sites, patriotic events and diverse cultures."

The ultra-conservative congresswoman Michele Bachmann is also toying with a run for the White House. She would be a wild card but could cause political mayhem among other candidates by giving voice to the frustrations of those Tea Partiers who think that the Republican leadership in Congress is betraying its pledge to slash and burn the budget.

The battle over government spending will provide the backdrop to the next 18 months of campaigning by both parties as the Republicans wrestle with just how far to push back against Obama's economic stimulus plans and how deep to cut.

Last week they were reminded just what dangerous territory this is. New York state voters elected a Democrat to a once-safe Republican congressional seat in rebellion over Republican plans to privatise Medicare, the government-funded health insurance programme for the over-65s. That election – prompted by the resignation of a married congressman caught trawling on websites for sex – has served as a warning to the Republicans that their takeover of the House of Representatives last year could prove to be a poisoned chalice at the next presidential election.

With House Republicans now leading the charge to slash government spending, the looming political battles over the budget risk offending an array of the party's constituencies that support cuts in principle but hate them when they intrude on their own interests.

But the Democrats are themselves far from invulnerable over spending. Last week, the senate unanimously rejected Obama's budget because the president had been forced to propose deeper cuts since the original plan was drawn up. Obama had originally proposed a three-year domestic spending freeze and an end to tax cuts for the wealthy, saving about $1.1tn over the next decade. But that did not go far enough for many Americans and Obama has since been forced to raise the cuts to $4tn.

In the wake of the New York state victory, Bill Clinton warned Democrats not to get cocky. For a start, he said, many voters do believe that the rapidly rising costs of Medicare need to be reined in – it's just that they just don't like the way the Republicans proposed to do it, which means that the Democrats have to come up with their own plan.

"You shouldn't draw the conclusion that the New York race means that nobody can do anything to slow the rate of Medicare costs," said Clinton. "You should draw the conclusion that the people made a judgment that the proposal in the Republican budget is not the right one. I agree with that."

It was a point taken up by the Democratic congressional campaign committee chairman, Steve Israel, who told NBC's television news programme Meet the Press: "This is a special election where Medicare was an overriding issue. We're going to stay with our gameplan."

Part of that plan is to play the "Bin Laden card" by portraying the president as tough and decisive, in order to counter a growing belief among many of his supporters that he has spent too much time seeking compromise and consensus and not enough time fighting for what he says he stands for.

Obama's campaign advisers plan to portray him as having made difficult decisions over the economy, Afghanistan and going after Bin Laden. Vice-president Joe Biden is already pushing that line: "We have a leader with the backbone of a ramrod," he told a political fundraiser last week.

Biden illustrated his point by describing how the president's decisiveness over getting Bin Laden had helped bring the real Obama "into focus". The vice-president said that while he was counselling hesitation, Obama gave the go-ahead for the raid that killed the al-Qaida leader.

"Presidential elections are about strength in leadership," said Biden. "The American people now have a crystal-clear picture of how strong and decisive our president is, and that's the last piece of the puzzle that had to be put in place."