In their Denver duel, the candidates contrasted their approach on taxes, the deficit and healthcare.
Barack Obama said he would ensure Americans were “playing by the same rules”. His rival said re-electing Barack Obama would continue a “middle-class squeeze”.
The president has held a narrow lead in recent opinion polls.
He went into the debate ahead in national polls and in many surveys in the swing states that will decide the election.
But he faced a confident opponent on the debate stage, with Mitt Romney, a former Massachusetts governor, sounding bullish throughout.
By contrast, the president at times appeared hesitant, occasionally asking moderator Jim Lehrer, of US public television network PBS, for time to finish his points.
Throughout the debate, each man attempted to paint his rival as a disaster for working American families.
They traded barbs on their economic plans, with Barack Obama describing his rival’s approach as “top-down economics” and a retread of Bush-era policies.
“If you think by closing [tax] loopholes and deductions for the well-to-do, somehow you will not end up picking up the tab, then Governor Romney’s plan may work for you,” he said.
“But I think math, common sense, and our history shows us that’s not a recipe for job growth.”
Mitt Romney derided Barack Obama’s policies as “trickle-down government”.
“The president has a view very similar to the one he had when he ran for office four years ago, that spending more, taxing more, regulating more – if you will, trickle-down government – would work,” Mitt Romney said.
“That’s not the right answer for America.”
Mitt Romney pledged not to reduce taxes for wealthy Americans, and said Barack Obama had misrepresented Romney’s tax plans on the campaign trail.
He hit out at the president for failing to cut the budget deficit in half as he pledged in 2008, and insisted that the US must not allow itself to go down the path of Greece or Spain.
Clashing repeatedly with Jim Lehrer over the time clock, Mitt Romney said that in order to reduce the $1.1tn US budget deficit he would repeal Barack Obama’s 2010 healthcare law and cut other unspecified programmes.
Barack Obama deflected criticism of his fiscal management, highlighting Mitt Romney’s pledge not to raise additional tax revenue. He said Mitt Romney’s approach to deficit reduction was “unbalanced” as a result.
“There has to be revenue in addition to cuts,” Barack Obama said.
On healthcare, Mitt Romney said that Barack Obama’s “Obamacare” reform law of 2010 had increased health costs and kept small businesses from hiring.
Even as he pledged to repeal Barack Obama’s health law, Mitt Romney praised and defended a plan he himself had previously signed as governor of Massachusetts that is widely hailed as the model for the Obama law.
Barack Obama, meanwhile, said his plan had kept insurance companies from denying coverage to sick people.
As the debate ended, each candidate’s allies rushed to talk up their man’s performance.
“The average person at home saw a president who you could trust,” Barack Obama adviser David Plouffe told reporters.
“That’s what the American people are looking for.”
But senior Mitt Romney aide Eric Fehrnstrom said the president had spoken “only in platitudes”.
“If this was a boxing match, it would have been called an hour into the fight,” he added.
The University of Denver debate was the first in a series of three presidential forums and one vice-presidential encounter this month.
Running-mates Joe Biden and Paul Ryan will meet in Danville, Kentucky on 11 October, before the second presidential debate on 16 October.
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