HEMPSTEAD, N.Y.—For most every question asked on Tuesday night, President Obama had two answers: the one about him, and the one about Mitt Romney.

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From the outset of their spirited 90-minute debate, Obama replied to each query both by spelling out his own policies and attacking Romney’s record or ideas.

After losing his first debate with Romney, Obama had no choice but to pull double-duty. He sought to undercut building support for his opponent among undecided voters, while allaying concerns about his own commitment within his own political base.

At the end, his staff and supporters felt relieved both on style and substance points, while Romney was quick off the stage and out of the debate hall.

Romney’s aides, though, felt in the long run that fact-checkers would declare their candidate the winner in the night's war of words.

The first question of the townhall-style debate at Hofstra University came from a 20-year-old college student, who asked Romney how he could assure him he would be able to support himself after graduation.

It was a tee-ball for a self-proclaimed turnaround artist running on the strength of his business record, and promising to accelerate the pace of the nation’s recovery from the Great Recession.

“Your question is one that’s being asked by college kids all over this country,” said Romney. “So, what we have to do is two things. We have to make sure that we make it easier for kids to afford college. And also make sure that when they get out of college, there’s a job.”

The Republican concluded: “It’s not going to be like the last four years. The middle-class has been crushed over the last four years, and jobs have been too scarce.”

When it was the president’s turn to speak, he assumed the mantle of the nation’s inspirational leader, proclaiming, “First of all, your future is bright.”

But barely 110-words later, during which he said he wanted to promote manufacturing jobs, Obama pivoted to his second answer: “Now, when Governor Romney said we should let Detroit go bankrupt, I said we’re going to bet on American workers and the American auto industry, and it’s come surging back.”

After Romney was given a chance to rebut, Obama replied, bluntly: “What Governor Romney said just isn’t true.”

The Democrat added: “And 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. 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.”

Those exchanges set the tone for the rest of the evening, which featured remarkable theatrics from two candidates used to talking about each other from a distance or before thousands of cheering supporters.

On Tuesday night, they walked around a stage before a group of 82 local questioners and hundreds more watching from the arena sidelines.

At points, the candidates spoke over each other and trailed one another across the floor, as they sought to have their opponent acknowledge their answer.

One in particular drew gasps, when Romney cut off the president of the United States by saying, “You’ll get your chance in a moment; I’m still speaking.”

Several of the questions had an almost comical pro-Obama tilt.

One focused on equal pay for women (a bill Romney once demurred about supporting). A second was about how Romney might differ from former President George W. Bush (a comparison he sought to avoid throughout the GOP primary campaign). A third centered on immigration (where Romney has encouraged “self-deportation”). And a fourth was on job outsourcing (an accusation leveled against companies Romney invested in while heading Bain Capital).

Nonetheless, Romney did not yield any quarter to Obama.

“The president’s statement of my policy is completely and totally wrong,” he said as he defended his contraception views in an answer typical of several he gave during the night.

Romney also seized the challenger’s prerogative, aiming to hold the incumbent accountable not for the promises he’s now making on the trail, but those he issued during his first campaign.

“The president has tried, but his policies haven’t worked,” the former Massachusetts governor said after a questioner who voted for Obama in 2008 said he was having doubts this time around.

“He’s great as a speaker and describing his plans and his vision. That’s wonderful, except we have a record to look at,” added Romney. “And that record shows he just hasn’t been able to cut the deficit, to put in place reforms for Medicare and Social Security to preserve them, to get us the rising incomes we need. Median income is down $4,300 a family and 23 million Americans out of work. That’s what this election is about. It’s about who can get the middle-class in this country a bright and prosperous future, and assure our kids the kind of hope and optimism they deserve.”

Romney also prospered as Obama avoided direct answers to two consecutive questions.

One man, who said he drafted a question with the help of his co-workers, asked simply and succinctly, Who was it that denied enhanced security for the US consulate in Benghazi, Libya, and why?

The president began, “Well, let me first of all talk about our diplomats...”

After paying homage to the late Ambassador Christopher Stevens and three other Americans killed in a Sept. 11 terrorist attack on the facility, Obama turned away from the answer to another attack on Romney.

“While we were still dealing with our diplomats being threatened, Governor Romney put out a press release, trying to make political points, and that’s not how a commander in chief operates,” said Obama.

When it was his turn to answer, Romney said: “It was a terrorist attack, and it took a long time for that to be told to the American people. Whether there was some misleading, or instead whether we just didn’t know what happened, you have to ask yourself why didn’t we know five days later, when the ambassador to the United Nations went on TV to say that this was a demonstration. How could we have not known?”

The next questioner also asked Obama about his vow, at the 2008 Democratic National Convention, to keep AK-47 assault rifles out of the hands of criminals.

“What has your administration done, or planned to do, to limit the availability of assault weapons?” the woman asked.

The president replied, “We’re a nation that believes in the Second Amendment, and I believe in the Second Amendment. We’ve got a long tradition of hunting and sportsmen and people who want to make sure they can protect themselves.”

After expressing anguish at having to comfort the families of mass shooting victims, Obama went on to say that he believed in enforcing the nation’s existing gun laws and possibly reintroducing an assault weapons ban.

But it took him 253 words to begin the sentence responding to the woman’s 16-word question.

Obama recovered in what turned out to be a closing statement.

He was given the last chance to answer after a man asked him and Romney to address the biggest misconception about themselves.

Romney, having escaped any mention all night of his assertion that 47 percent of Americans believe they are “victims” who deserve government handouts, brought up the remark as he asserted he is not the heartless person he is sometimes depicted.

“I want 100 percent of the American people to have a bright and prosperous future,” he said.

Obama disputed the caricature that he believes in big government and doubts the free enterprise system. Then he pivoted to an attack on Romney.

“I believe Governor Romney is a good man, loves his family, cares about his faith,” the president added. “But I also believe that when he said behind closed doors that 47 percent of the country considered themselves victims who refuse personal responsibility, think about who he was talking about: Folks on Social Security who’ve worked all their lives. Veterans who’ve sacrificed for this country. Students who are out there trying to hopefully advance their own dreams, but also this country’s dreams. Soldiers who are overseas fighting for us right now. People who are working hard every day, paying payroll tax, gas taxes, but don’t make enough income.”

Obama concluded: “I want to fight for them. That’s what I’ve been doing for the last four years. Because if they succeed, I believe the country succeeds.”

His last answer, like his first, had two parts: the one about him and the one about his opponent.