Rivals Bring Bare Fists to Rematch

President Obama and Mitt Romney engaged Tuesday in one of the most intensive clashes in a televised presidential debate, with tensions between them spilling out in interruptions, personal rebukes and accusations of lying as they parried over the last four years under Mr. Obama and what the next four would look like under a President Romney.

Competing for a shrinking sliver of undecided voters, many of them women, their engagements at times bordered on physical as they circled each other or bounded out of their seats while the other was speaking, at times more intent to argue than to address the questions over jobs, taxes, energy, immigration and a range of other issues.

Mr. Obama, criticized by his own party for a lackluster debate performance two weeks ago, this time pressed an attack that allowed him to often dictate the terms of the debate. But an unbowed Mr. Romney was there to meet him every time, and seemed to relish the opportunity to challenge a sitting president.

Mr. Obama’s assertive posture may well have stopped the clamor of concern from supporters that had been weighing on his campaign with three weeks and one more debate to go before the election.

The president’s broadsides started with a critique of Mr. Romney for his opposition to his administration’s automobile bailout in his first answer — “Governor Romney said we should let Detroit go bankrupt” — and ended more than 90 minutes later with an attack on Mr. Romney’s secretly taped comments about the “47 percent” of Americans who he said did not take responsibility for their own lives.

“When he said behind closed doors that 47 percent of the country considers themselves victims who refuse personal responsibility — think about who he was talking about,” the president said toward the end of the debate at Hofstra University in Hempstead, N.Y.

It was as if a different, highly charged president had taken the stage rather than the reluctant, disengaged-seeming candidate who showed up to meet Mr. Romney at their first debate two weeks ago.

Mr. Romney stayed acutely focused on Mr. Obama’s record in the face of it all, saying that the president had failed to deliver what he promised in his 2008 campaign and arguing repeatedly and strenuously, “We just can’t afford four more years like the last four years.”

He credited Mr. Obama for being “great as a speaker and describing his vision.” But then he brought down the ultimate hammer in a challenge to an incumbent: “That’s wonderful, except we have a record to look at. And that record shows he just hasn’t been able to cut the deficit, to put in place reforms for Medicare and Social Security to preserve them, to get us the rising incomes we need.”

The two took pains to fashion their arguments toward female voters, with the debate seeming at times directed entirely at them. Mr. Obama mentioned Mr. Romney’s vow to cut government funding for Planned Parenthood at least four times; Mr. Romney repeatedly mentioned that under Mr. Obama: “There are three and a half million more women living in poverty today than when the president took office. We don’t have to live like this.”

And Mr. Romney sought to broaden his appeal to women by softening his tone on reproductive issues, saying: “Every woman in America should have access to contraceptives.”

Emphasizing his record of diversity as governor based on his own recruiting, he said, “I brought us whole binders full of women.”

It is a bit of conventional wisdom that undecided voters seek comity in their leaders. There was none of that Tuesday.

At times the back and forth was personal in small ways. Having already invoked the 14 percent effective tax rate that Mr. Romney personally paid, Mr. Obama mentioned Mr. Romney’s investment in Chinese companies. Then Mr. Romney asked if Mr. Obama had looked at his own pension for its investments.

“I don’t look at my pension,” Mr. Obama said. “It’s not as big as yours.”

But at other moments the verbal sparring took on a deeper, emotional resonance, such as when Mr. Romney suggested that the administration was intentionally misleading in its shifting explanations for the attack on the American mission in Benghazi, Libya, that resulted in the deaths of the American ambassador, J. Christopher Stevens, and three other Americans there.

“The suggestion that anybody in my team, whether the secretary of state, our U.N. ambassador, anybody on my team would play politics or mislead when we’ve lost four of our own, Governor, is offensive,” Mr. Obama said, standing and looking intently at his opponent. “That’s not what we do. That’s not what I do as president.”

Mr. Obama noted that he had gone to the Rose Garden the day after the attack to say “this was an act of terror.”