Republican Mitt Romney, looking to jolt his struggling presidential campaign, accused Barack Obama of misrepresenting his positions as the two candidates shared a stage for the first time in a high-stakes presidential debate.

With the long campaign entering its final month, Romney needed a strong showing in the debate before tens of millions of television viewers as polls show him falling behind the president in what has been a tight race.

It is not clear what effect, if any, the debate will have. But Romney, often seen as wooden and lacking passion, seemed more at ease than Obama. In a rare post-debate concession, some Democratic strategists not involved in the campaign conceded the president was not at his best and missed opportunities to challenge his rival.

Romney was clearly on the offensive, blaming Obama for the weak U.S. economy — the biggest issue in the campaign. "Going forward with the status quo is not going to cut it for the American people who are struggling today," Romney said.

He repeatedly accused Obama of misstating his positions, virtually lecturing him at one point after the president accused him of seeking to cut education funds. "Mr. President, you're entitled to your own airplane and your own house, but not your own facts."

Obama sparred back, accusing Romney, a former Massachusetts governor, of seeking to "double down" on economic policies that led to the devastating economic downturn four years ago — and of evasiveness when it came to prescriptions for tax changes, health care, Wall Street regulation and more.

After Romney said he would repeal and replace regulations passed after the 2008 financial crisis, Obama responded: "Does anyone think there is too much oversight and regulation of Wall Street? Because if you do, then Gov. Romney is your candidate."

Obama, a former legal scholar, seemed somewhat professorial at times. He avoided themes that his campaign has used against Romney, including criticism of Romney's private equity firm, Bain Capital, which the Democrat has demonized as a corporate predator. Obama also did not mention that Romney has personal assets in Swiss bank accounts.

More surprisingly, Obama made no reference to a widely publicized secret recording of Romney, in which he said that 47 per cent of Americans view themselves as victims who depend on the government and refuse to take responsibility for their lives.

No game-changing gaffes

The debate, the first of three this month, had been widely anticipated. Polls showed that the public expected Obama, a gifted speaker, had an advantage over Romney, and Romney's campaign pushed that viewpoint to lower expectations for their candidate.

Neither candidate appeared to make any major gaffes likely to change the course of the race.

President Barack Obama said Mitt Romney wants to return to the policies that hurt the U.S. economy. (Eric Gay/Associated Press)

At times the debate turned into rapid-fire charges and retorts that drew on dense facts and figures that were difficult to follow.

The men argued over oil industry subsidies, federal spending as a percentage of the GDP, cuts to the health-care program for the elderly, taxes and small businesses and the size of the federal deficit and how it grew.

The candidates' answers reflected their general philosophical differences.

Romney and fellow Republicans see the federal government as too big, taxing Americans excessively, running up deficits and hindering job creation through unnecessary regulations.

Obama and his fellow Democrats see government as a potential force for good, providing the infrastructure and education needed in a dynamic economy and giving even poor Americans the opportunity to succeed.

While debates haven't historically altered the course of a presidential campaign, millions of Americans tune in for them — as many as 60 million were expected to have watched on Wednesday — they can often change public perceptions of a politician.

There have been nine sets of presidential debates since the first televised event in 1960 between Richard Nixon and John F. Kennedy.

Nixon, recovering from knee surgery, perspired so profusely that it was thought to have cost him the election as, post-debate, Kennedy squeaked past him in the polls. In 2000, George W. Bush overtook Al Gore following their debates after Bill Clinton's vice-president appeared condescending and petulant during their exchanges.

But those were the only two instances in which the politician trailing in the race came from behind, post-debate, to win the election. Romney is hoping to become the third, and several conservative pundits predicted Wednesday's debate will put serious wind in his sails.

Quick moment of laughter

The debate began on a friendly note.

Republican presidential nominee Mitt Romney said during the debate that going forward with 'the status quo' won't cut it for struggling Americans. (Charlie Neibergall/Associated Press)

The two rivals clasped hands and smiled as they strode onto the debate stage at the University of Denver, then waved to the audience before taking their places behind identical podiums. They faced questions from moderator Jim Lehrer of PBS.

There was a quick moment of laughter when Obama referred to first lady Michelle Obama as "sweetie" and noted it was their 20th anniversary.

Romney added best wishes, and said to the first couple, "I'm sure this is the most romantic place you could imagine, here with me."

Though election day is more than a month away, many Americans have already started casting ballots because some states allow early voting. That put extra pressure on Romney to come up with a showing strong enough to alter the course of the campaign.

The next two debates are Oct. 16 in New York and Oct. 22 in Florida.

Vice-President Joe Biden and Romney's running mate, congressman Paul Ryan, have one debate in Kentucky on Oct. 11.