(CBS News) As the second presidential debate kicked off Tuesday night, President Obama was quick to go on offense against Republican presidential nominee Mitt Romney, taking him to task over claims he deemed to be false and accusing him of having a "one-point plan" for the country: "To make sure that folks at the top play by a different set of rules."
Both candidates were spirited out of the gate, sparring over questions about taxes, job growth, education, and women's health, and engaging in various points in heated exchanges over energy policy and immigration.
Mr. Obama, who was panned in the first debate for a performance that was cast as lackluster and passive, attempted to paint the candidate as out-of-touch with average Americans, and was aggressive in targeting Romney over his "five-point plan" to grow 12 million jobs.
"Governor Romney's says he's got a five-point plan? Governor Romney doesn't have a five-point plan. He has a one-point plan," Mr. Obama said. "And that plan is to make sure that folks at the top play by a different set of rules. That's been his philosophy in the private sector, that's been his philosophy as governor, that's been his philosophy as a presidential candidate."
"The last thing we need to do is go back to the exact same policies that got us there," he said.
Romney, meanwhile, defended his tax proposal, combating the charge that his proposal is mathematically impossible.
"Well of course they add up," said Romney, when asked what he would do if they did not. "I was someone who ran businesses for 25 years, and balanced the budget. I ran the Olympics and balanced the budget. I ran the state of Massachusetts as a governor, to the extent any governor does, and balanced the budget all four years."
Romney did not provide further information regarding the details of his proposal, pivoting instead to an attack of Mr. Obama's record.
"When we're talking about math that doesn't add up, how about $4 trillion of deficits over the last four years, $5 trillion? That's math that doesn't add up," he said. "And then we have his own record, which is we have four consecutive years where he said when he was running for office, he would cut the deficit in half. Instead he's doubled it. We've gone from $10 trillion of national debt, to $16 trillion of national debt. If the president were reelected, we'd go to almost $20 trillion of national debt. This puts us on a road to Greece."
On immigration, Mr. Obama repeatedly targeted Romney for having suggested in the past that imposing a policy of "self-deportation" would serve as an effective way to reduce illegal immigration, while Romney noted that Mr. Obama has not made good on a campaign promise to implement immigration reform.
The debate has been touted as a high-stakes affair for both candidates, as Mr. Obama attempts to make up ground lost after the first matchup, and Romney tries to hold on to a recent wave of momentum.
In the 13 days since the two men last faced off, Romney has seen a much-needed boost in the polls, changing the dynamic in a race that had previously looked all but over for the former Massachusetts governor.
Now, amid a panoply of polls showing a wide range of often disparate results, the main - and possibly only - clear consensus is that the race is very close.
The debate was held at Hofstra University in Hempstead, N.Y. Just a handful of the 82 audience members, all of whom were selected by the Gallup Organization to represent a variety of socio-economic, racial and political backgrounds, were able to ask the candidates questions.
© 2012 CBS Interactive Inc. All Rights Reserved.