PRESIDENT Barack Obama put his re-election bid back on a firm footing with a strong debating performance that is likely to thrill his supporters and earn him a second look from the few voters who remain undecided.

With the election three weeks away, Mr Obama's second of three debates with Mitt Romney represented one of the final chances to make an impression with voters.

The President made the most of it with a focused, aggressive effort. It was a sharp departure from his listless first debate two weeks ago, when Romney's dominant performance ignited a resurgence by the Republican that left the race virtually even heading into Tuesday's match-up.

"Game on – he's back," Carleton College political science professor Steven Schier said of the President.

Mr Obama made sure to work in all of the attack lines he had neglected in the first debate.

The President also outlined the accomplishments of his first term – from saving the car industry to killing Osama bin Laden – and framed his answer to a question on women's rights in movingly personal terms.

Mr Romney had his moments, especially when describing promises Mr Obama had made and not kept. The Republican avoided the type of rout Mr Obama suffered in the first debate, but the night belonged to the President, analysts said.

Flash polls after the debate pointed to an Obama win. Meanwhile, his odds for re-election on the In-trade prediction market, which allows people to buy or sell shares in real-life events, climbed 1.6% points, to 63.6%.