"What Governor Romney said just isn't true," Obama said tonight after the Republican presidential nominee said he opposed bailing out carmakers because he wanted the industry to go through the same type of bankruptcy experienced by other major companies.
Obama said Romney's plan was to take General Motors Co (GM) and Chrysler Group LLC "into bankruptcy without providing them with any way to stay open, and we would have lost one million jobs".
The two rivals often interrupted each other while circling the stage as moderator Candy Crowley of CNN tried to keep the debate on track. As Romney went after Obama by saying that his administration had cut oil production, Obama interrupted, saying "not true, Governor Romney," or "it's just not true".
The interjections spurred Romney to say, "you’ll get your chance in a moment -- I’m still speaking," drawing a gasp from the debate audience, which had been told to stay quiet.
The 90-minute debate at Hofstra University in Hempstead, New York, took on added urgency for Obama after polls showed he lost the first showdown, giving Romney's campaign a surge of energy and gains in national and state polls. The two candidates took questions from undecided voters.
Romney attacked Obama on foreign policy, saying that he had not done enough to protect the consulate in Benghazi before the Sept 11 attack that killed four Americans including the US ambassador to Libya. The former Massachusetts governor also criticised Obama for taking too long to dispel the idea that the attack was caused by a spontaneous demonstration instead of terrorists.
Obama said he is "ultimately responsible" for what goes on at US diplomatic missions.
The suggestion that "anybody on my team would play politics or mislead when we've lost four of our own, Governor, is offensive," Obama said. "That's not what I do as president. That's not what I do as commander-in-chief."
After Obama said he had called the attack an act of terror the next day, Romney said, "I want to make sure we get that for the record, because it took the president 14 days before he called the attack in Benghazi an act of terror."
Obama let him go on and then said, "get the transcript." Crowley intervened to say that Obama was indeed correct about using that term in remarks in the White House Rose Garden he made about the attack.
The president used the term in a general reference to his efforts to combat terrorism, and administration officials continued to blame protesters for the attack in Libya for days afterward.
The two clashed over China, with Romney criticising Obama for failing to do enough to prevent currency manipulation in the country. Obama responded that Romney, who has stressed his business credentials as a private-equity executive, had invested in companies that were "pioneers of outsourcing" to China.
"You're the last person who's going to get tough on China," Obama said to Romney.
Romney returned to the question later, saying his investments were in a blind trust and included investments outside the US "Have you looked at your pension?" Romney asked Obama.
"You know, I don't look at my pension," Obama replied. "It's not as big as yours, so it doesn't take as long," he added, to laughter.
Both candidates pledged that their overall economic plans would create more US jobs after the opening question in the debate's town-hall format came from a college student who was concerned about future employment.
"More debt and less jobs, I'm going to change that," Romney said of Obama's record. "I know what it takes to create good jobs again."
Obama, who was criticised for not laying out a clear vision during the Oct 3 debate between the two, began by telling the student, "your future is bright."
Romney said he wanted to bring tax rates down and simplify the tax code. In the process, he floated the idea of capping deductions at $25,000. Earlier, he had suggested $17,000.
Obama went after Romney for proposing tax cuts while saying he would reduce the federal deficit, without giving specifics. Referring to Romney’s history as a private equity executive, Obama said he wouldn't have taken such a "sketchy deal" without details.
"And neither should you, the American people, because the math doesn't add up," Obama said.
Romney countered, "of course they add up," and said Obama was misconstruing his plan.
On social issues, Obama said Romney would let employers make decisions about whether or not contraception should be covered through insurance for women.
"Every woman in America should have access to contraceptives, and the president's statement of my policy is completely and totally wrong," Romney said.
Obama went on to say that Romney's positions on issues such as Medicare, immigration and federal funding for Planned Parenthood took him beyond the stances of former Republican President George W Bush. "In some ways, he's gone to a more extreme place," Obama said.
Romney trumpeted his efforts during his 2003 to 2007 gubernatorial term to find women for his Cabinet.
"I went to a number of women's groups and said, 'Can you help us find folks' and they brought us whole binders full of women," he said.
Obama used his last comments of the debate, when Romney would not have a chance to respond, to bring up his rival's comments at a private fundraiser in May in which he branded 47% of Americans as government-dependent "victims." Those people include Social Security recipients, veterans and students, "and I want to fight for them," Obama said.
Romney, in his closing remarks before Obama spoke, stressed that he wanted to help "100%" of the American people.