HEMPSTEAD, N.Y. — An aggressive President Barack Obama accused challenger Mitt Romney of favoring a "one-point plan" to help the rich and leveling offensive criticism about the recent deadly terrorist attack in Libya Tuesday night in a debate crackling with energy and emotion just three weeks before the election.

Romney pushed back hard, saying the middle class "has been crushed over the last four years," that 23 million Americans are struggling to find work and that the death of the U.S. ambassador to Libya was part of an unraveling of the administration's foreign policy.

The president was feistier from the outset than he had been in their initial encounter two weeks ago, when he turned in a listless performance that sent shudders through his supporters and helped fuel a rise by Romney in opinion polls nationally and in some battleground states.

Obama challenged Romney on economics and energy policy, accusing him of switching positions and declaring that his economic plan was a "sketchy deal" that the public should reject.

Romney gave as good as he got.

"You'll get your chance in a moment. I'm still speaking," the former Massachusetts governor said at one point while Obama was mid-sentence. He said the president's policies had failed to jumpstart the economy and crimped energy production.

The open-stage format left the two men free to stroll freely across a red-carpeted stage, and they did. Their clashes crackled with energy and tension, and the crowd watched raptly as the two sparred while struggling to appear calm and affable before a national television audience.

The rivals disagreed about taxes, measures to reduce the deficit, energy, pay equity for women and health care issues. Immigration prompted yet another clash, Romney saying Obama had failed to pursue the comprehensive legislation he promised at the dawn of his administration, and the president saying Republican obstinacy made a deal impossible.

Under the format agreed to in advance, members of an audience of 82 uncommitted voters posed questions to the president and his challenger.

Nearly all of them concerned domestic policy until one raised the subject of the recent death of the U.S. ambassador to Libya in a terrorist attack at an American post in Benghazi.

Romney said it took Obama a long time to admit the episode had been a terrorist attack, but Obama said he had said so the day after in an appearance in the Rose Garden outside the White House.

When moderator Candy Crowley of CNN said the president had in fact done so, Obama, prompted, "Say that a little louder, Candy."

Secretary of State Hillary Clinton has taken responsibility for the death of Ambassador L. Christopher Stevens and three other Americans, but Obama said bluntly, "I'm the president and I'm always responsible.

Romney said it was "troubling" that Obama continued with a campaign event in Las Vegas on the day after the attack in Libya, an event he said had "symbolic significance and perhaps even material significance."

Obama seemed to bristle. He said it was offensive for anyone to allege that he or anyone in his administration had used the incident for political purposes. "That's not what I do."