HEMPSTEAD, NY -- President Obama sought to regain his re-election momentum Tuesday in a second debate with Republican Mitt Romney, tangling with his rival over jobs, the auto industry bailout, energy, taxes and other issues.

The two put on a more heated and energetic show than in their first debate, often questioning or interrupting each other and disputing the other's claims. Both men walked the stage, each speaking directly to their questioners and gesturing to each other.

Obama, criticized after the first debate for looking down at his notes and appearing disengaged, watched Romney intently when he spoke.

After seeing an aggressive Romney score gains in polls following their initial encounter Oct. 3, Obama entered the debate intending to show more passion and make his case to the nation for a second four-year term.

He used the first question from the audience of uncommitted voters, which was about jobs, to blast Romney's opposition to the bailout of two of the three big U.S. automakers. Obama said that if Romney's way had prevailed, bankruptcy would have cost a million Americans their jobs.

Obama ridiculed Romney's claim to have a five-point plan to create jobs.

"He doesn't have a five-point plan, he has a one-point plan, and that's to make sure people at the top play by different rules. ... That's been his philosophy," Obama said.

"The last thing we need to do is go back to the same policies" that put the nation into an economic downturn four years ago, Obama said.

Romney blamed Obama for the economy's failure to generate more jobs.

"The president's policies have been exercised over the last four years, and they haven't put people back to work," he said.

Romney said of the automobile industry bailout that going through the bankruptcy process "was precisely what I recommended and ultimately what happened."

Obama responded immediately that "What the governor just said isn't true. He wanted to take them into bankruptcy without providing them any way to stay open." Obama said that without the government bailout he supported, "we would have lost a million jobs."

The high-stakes matchup came just three weeks before the Nov. 6 general election and as some states have already begun allowing voters to cast ballots by mail.

The duo battled at length over taxes, and the calculus behind Romney's tax cut plans.

Romney repeated his campaign position that he will cut taxes for the middle class and lower rates 20% across the board without adding to the deficit. He declined to name loopholes and deductions he would eliminate as a way to recover the revenue lost by the lower rates.

"I'm going to bring rates down across the board. ... I'm not going to have people at the high end paying less than they pay now," he said. "I will not under any circumstances increase taxes on the middle class."

Obama responded that if someone had gone to businessman Romney with a plan like his own -- proposing to cut $8 trillion in revenue without specifying how he would recoup the lost dollars -- the idea would be laughed at as unbelievable.

"You wouldn't have taken such a sketchy deal, and neither should the American people, because the math doesn't add up," Obama said.

Obama reminded the audience that in the two years of tax returns Romney has made public, he paid 14% in federal taxes -- a rate far below most middle-income families despite his wealth and an annual income in excess of $20 million.

Romney pointed to his record in business as he insisted that his administration would find a way to make his tax and economic policies work.

"Of course they add up," he said. "I was someone who ran businesses for 25 years and balanced the budget. I ran the Olympics and balanced the budget."

"I know what it takes to make an economy work," Romney said. "An economy with 23 million people looking for work, that's not a good economy."

The former Massachusetts governor was questioned by a woman in the audience who said she blamed former president George W. Bush's policies for much of the economic difficulty of the past four years and wanted to know what Romney would do differently from Bush.

Romney responded by saying he would balance the federal budget and have tougher policies toward China.

"I'll crack down on China," Romney said. "President Bush didn't."

Obama responded: "Governor, you're the last person who's going to get tough on China." He said his administration has pressed twice as many trade complaints against China than Bush did.

Obama said Romney was more extreme than Bush, noting that the former president did not try to cut off federal support for Planned Parenthood as Romney has promised.

" In some ways he's gone to a more extreme place when it comes to social issues," Obama said of Romney.

They spoke in a town-hall-style meeting at Hofstra University before an audience of registered and undecided voters from Nassau County, N.Y.

(USA Today)