By Andy Sullivan
WASHINGTON (Reuters) - President Barack Obama put his re-election bid back on firm footing on Tuesday night with a strong debate performance that is likely to thrill his Democratic supporters and earn him a second look from the few voters who remain undecided.
With the November 6 election three weeks away, Obama's second of three debates with Republican rival Mitt Romney represented one of the final chances to make an impression with voters.
Obama 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 matchup.
"Game on - he's back," Carleton College political science professor Steven Schier said of the president.
Obama made sure to work in all of the attack lines he had neglected in the October 3 debate.
He hammered Romney for the wealthy Republican's low personal income tax rate and Romney's now-infamous dismissal of "47 percent" of the electorate, as seen in a secretly recorded video of the former Massachusetts governor.
Obama also crisply outlined the accomplishments of his first term in office - from saving the auto industry to killing Osama bin Laden - and framed his answer on a question about women's rights in movingly personal terms.
Romney had his moments as well, especially when describing promises Obama had made and not kept.
Romney avoided the type of rout that Obama suffered in the October 3 debate, but the night belonged to the president, analysts said.
"I'd say it's a clear win for Obama," said Boston University communications professor Tobe Berkovitz. "Certainly it would be difficult for anyone to say Romney won this debate."
Flash polls taken after the debate pointed to an Obama win. Meanwhile, Obama's odds for re-election on the Intrade prediction market climbed 1.6 percentage points, to 63.6 percent.
'A BIT OF A BOUNCE'
Debates have rarely affected the outcome of U.S. presidential elections, but this year may prove an exception.
Romney silenced critics in his own party and reversed a month of missteps with a strong performance in the first debate. A week later he had wiped out Obama's lead in opinion polls.
That "bounce" for Romney has slipped in recent days, according to Reuters/Ipsos tracking polls. Obama led Romney by 3 percentage points in the daily Reuters/Ipsos poll on Tuesday.
"This will give the president a bit of a bounce and a little bit of an edge, but it's going to be quite close right down to the wire," said Notre Dame University political science professor Michael Desch.
The final presidential debate, scheduled for Monday in Boca Raton, Florida, probably will matter less.
Some 10 percent of voters have cast their ballots already, according to Reuters/Ipsos polling data, and that figure will climb sharply as both campaigns kick their get-out-the-vote operations into gear and urge supporters to take advantage of state laws that allow early voting.
Foreign policy, the topic of next week's debate, takes a distant back seat to economic concerns for most voters.
It was a foreign policy discussion that led to Romney's most uncomfortable moment on Tuesday night, as he bungled what could have been an opportunity to plant doubts in voters' minds about Obama's handling of the attacks on diplomatic facilities in Libya last month.
Romney had hoped to use the incident to erode Obama's national security credentials. Instead, he battled with the moderator, CNN's Candy Crowley, over whether he was accurately characterizing Obama's remarks about whether the incident was a terror attack.
The exchange left Romney aides fuming at Crowley, while Obama was able to avoid the question of whether his administration had protected the facility adequately.
OBAMA'S DEFT MANEUVERING
Obama also danced around other questions that could have tripped him up.
He turned a question about gun control - an unpopular issue for voters in many battleground states - into an opportunity to point out Romney's shifting positions on the issue.
Obama responded to a question about gas prices by noting that they had been low when he took office only because of the recession that he inherited.
"It's conceivable that Governor Romney could bring down gas prices, because with his policies we'd be back in that same mess," he said, drawing laughter from the crowd.
Aside from his blown opportunity on Libya, Romney did not do poorly. He reminded viewers that Obama had failed to fulfill promises to cut the deficit in half and introduce immigration-reform legislation, and warned that too many people are still out of work.
"If you elect President Obama you know what you're going to get," he said. "You're going to get a repeat of the last four years."
Romney's performance probably did not hurt his chances of winning the White House, analysts said. But Obama probably boosted his odds by turning in the focused, aggressive performance that his supporters had hoped to see in the first debate.
"They're thinking, 'We're back in the ball game,' " said Robert Lehrman, a former speech writer for Democratic vice president Al Gore who now teaches at American University.
"It wasn't that Romney got worse - Obama got a lot better."
(Editing by David Lindsey and Eric Walsh)