President Barack Obama rebounded from a lackluster performance in the first presidential debate in the rematch Tuesday night, frequently challenging Republican nominee Mitt Romney in a town hall-style faceoff at Hofstra University.

Flashing an aggressiveness that was largely absent in the first round, Obama repeatedly rebutted Romney when he felt the Republican nominee had twisted the facts. After Romney said his call to guide the auto industry through a managed bankruptcy was essentially the same as Obama’s plan for Detroit, the president flatly stated that, “what Governor Romney said just wasn’t true.”

Throughout the debate, Obama returned to a theme that has been central to his campaign trail pitch: that Romney represents a return to ruinous economic policies that helped drive the country into a recession. When Romney noted that gas prices had risen precipitously since the start of Obama’s term, the president suggested that prices were low in early 2009 because of a recession brought on “as a result of some of the same policies Governor Romney is now promoting.”

“We have been digging our way out of policies that were misplaced and focused on the top doing very well and middle class folks not doing very well,” Obama said later.

For his part, Romney stuck largely to assailing Obama’s legacy of fitful economic growth. He returned to the point that his experience in the private sector would better position him to foster prosperity for all.

“I know why jobs come and jobs go, and they’re going because of the policies of this administration,” Romney said.

But the former Massachusetts governor struggled at times to offer detailed policy prescriptions, most notably when it came to his plan to lower tax rates without increasing the deficit. When an audience member asked Romney which deductions he would limit to offset the tax cuts, he was unable to offer specifics. He did call for a repeal of taxes on dividends, interest and capital gains.

Obama and his allies have argued that it is impossible to institute an across-the-board tax cut, as Romney advocates, without raising taxes on the middle class. He depicted Romney’s tax plan as a gift to affluent Americans and backed a plan that combines spending cuts with ensuring that “the wealthy do a little more.”

“When he’s asked ‘how are you going to do it, which deductions, which loopholes are you going to close, he can’t tell you,” Obama said in reference to Romney, adding that “We haven’t heard any specifics beyond Big Bird and eliminating funding for Planned Parenthood.”

Energy policy also played a prominent role, reflecting anxiety about spiraling gas prices. Romney charged that Obama was undermining American energy independence – something Romney said he would deliver within eightyears -- by cutting back on coal production, suspending the construction of the Keystone XL oil pipeline from Canada and failing to adequately expand oil and gas exploration.

“I will fight for oil and coal and natural gas, and the proof for whether a strategy is working or not is the price of what you’re paying at the pump,” Romney said.

But Obama noted that American oil and natural gas production have surged to their highest levels in years and rejected Romney’s contention that his administration has blocked expanded drilling on public lands, noting that he had withdrawn unused drilling leases energy companies had been sitting on. He reiterated his commitment to higher fuel efficiency standards in automobiles and investments in new forms of energy, saying it was a matter of ensuring America’s competitive advantage.

“We can’t just produce traditional sources of energy. We have to look to the future,” Obama said, adding that, “If we’re only talking about tomorrow and the next day and not thinking 10 years from now we’re not going to control our economic future, because China and Germany, they’re making those investments.”

On immigration, Romney doubled down on his commitment to streamlining legal immigration while cracking down on illegal immigration. He called for legislation offering green cards to foreign students who obtain advanced degrees and for tighter penalties on businesses that hire undocumented immigrants.

“I will not grant amnesty to those who come here illegally,” Romney said, rejecting “magnets,” such as offering drivers' licenses to undocumented workers, that offer an incentive for illegal immigration.

Obama responded by highlighting his work to tighten border security and refocus enforcement on immigrants with criminal records (Obama has presided over more deportations than any other American president). He also touted an administration policy that allows undocumented immigrants who were brought to the country as children to avoid deportation, contrasting the approach with the hardline immigration stance Romney advocated while seeking the Republican nomination.

“His main strategy during the Republican primary was to say we’re going to encourage self-deportation, making life so miserable for folks that they leave,” Obama said, noting that Romney has sworn to veto the DREAM Act and enlisted Kansas Secretary of State Kris Kobach, author of Arizona’s controversial immigration law, as a campaign adviser.

Both campaigns have pushed hard to court female voters, and they had multiple opportunities on Tuesday night. Obama responded to a question about ensuring equal pay by noting his support for the Lily Ledbetter Fair Pay Act, while Romney underscored his efforts to appoint women while governor of Massachusetts and noted that women had suffered massive job losses under Obama.

Obama also revived a dispute about a section in the Affordable Care Act mandating that all insurance plans cover contraception. Republicans said that measure interfered with the religious freedom of institutions like Catholic hospitals and universities, a critique that Romney backed.

“A major difference in this campaign is that governor Romney feels comfortable having politicians in Washington deciding the health care choices that women are making,” Obama said.