* Obama and Romney clash over Libya killings
* Candidates circle, confront each other on stage
* Polls show race deadlocked with three weeks left
By John Whitesides and Samuel P. Jacobs
HEMPSTEAD, N.Y., Oct 16 (Reuters) - U.S. President Barack Obama aggressively challenged Republican candidate Mitt Romney on jobs, energy and Libya in their second debate on Tuesday as the Democrat tried reclaim the momentum in a tight White House race.
Obama was much sharper and more energetic than in their first debate two weeks ago, when his listless performance was heavily criticized and gave Romney's campaign a much-needed boost.
The incumbent fought back against Romney's accusations that he had played down the attack by Islamist militants in Libya last month that killed four Americans, including the U.S. Ambassador Chris Stevens.
"I'm the president and I'm always responsible," Obama said.
The two men argued over whether the White House had described the Benghazi attack as terrorism or not, with Obama saying he had in fact called it an act of terror when he spoke in the Rose Garden the following day.
Romney accused his rival of overseeing a stagnant economy. "The middle class has been crushed over the last four years and jobs have been too scarce," the former Massachusetts governor said.
"I know what it takes to get this economy going," he said. "I know what it takes to create good jobs again."
Gamblers seemed to think Obama did well at the debate, in which undecided local voters from New York state's Nassau County asked questions in an intimate town-hall format.
Online betting site Intrade showed Obama had a 64.4 percent chance of winning the election after the debate compared to 35.5 percent for Romney. Before they met, Obama led by 62.2 percent to 37.8 percent.
Obama repeatedly accused Romney of misstating his policies as president, and resurrected his charge that the economic proposals put forward by the former private equity executive were designed to protect and bolster the wealthy at the expense of the middle class.
"Governor Romney says he's got a five-point plan. Governor Romney doesn't have a five-point plan, he has a one-point plan. And that plan is to make sure that folks at the top play by a different set of rules," Obama said in the debate at Hofstra University in Hempstead, New York.
Both candidates roamed the stage to talk directly to the questioners. At times they circled each other warily at center stage like prize fighters, talking over each other and bickering frequently about the rules and who had exceeded their time.
Romney confronted Obama face-to-face at one point to ask repeatedly if licenses and permits for energy drilling on federal land had been reduced during his administration. The Republican's strong performance in the first debate helped him reverse his slide in the polls, and recent surveys have put the race for the White House at a virtual dead heat just three weeks ahead of the Nov. 6 election.
Obama seems to have stopped the slide after the last debate. In a Reuters/Ipsos daily tracking poll on Tuesday, he gained a bit more ground on Romney for the third straight day and led 46 percent to 43 percent. But a Gallup/USA Today poll showed Romney ahead by 4 percentage points in the 12 most contested states.
After being criticized for his passive performance in the first debate, Obama attacked Romney repeatedly this time. He criticized his opposition to a bailout for the auto industry, ridiculed his claim he would get tough on China and compared him unfavorably to unpopular former Republican President George W. Bush.
"George Bush didn't propose turning Medicare into a voucher. George Bush embraced comprehensive immigration reform. He didn't call for self-deportation. George Bush never suggested that we eliminate funding from Planned Parenthood," Obama said.
"So, there are differences between Governor Romney and George Bush but they are not on economic policies. In some ways he's gone to a more extreme place when they come to social policies," Obama said.
The two also clashed over the auto bailout, with Romney saying Obama had misrepresented his position that General Motors should go into a managed bankruptcy.
"He keeps saying, you want to take Detroit bankrupt. Well, the president took Detroit bankrupt," Romney said. "You took General Motors bankrupt. You took Chrysler bankrupt. So when you say that I wanted to take the auto industry bankrupt, you actually did."
Obama responded: "What Governor Romney said just isn't true. He wanted to take them into bankruptcy without providing them any way to stay open. And we would have lost a million jobs."
Obama rejected the notion that Romney was more supportive of finding more energy sources like coal and natural gas.
" When you were governor of Massachusetts, you stood in front of a coal plant and pointed at it and said 'This plant kills,' and took great pride in shouting it down. And now suddenly, you're a big champion of coal," Obama said.