Chief correspondent

As he campaigns through the battleground states in the final hours of Campaign 2012, President Obama tells every audience, “You know where I stand and you know what I believe.” But on election eve, there is still an unanswered question about the president: How would the experience of his first term inform and shape a second?

The voters will decide Tuesday whether Obama gets that second term. He appeared to have a slight advantage on the last full day of campaigning but not one big enough to let his supporters relax. As Columbus Mayor Michael B. Coleman put it on his way into the Nationwide Arena before an Obama rally Monday afternoon, “I’m confident but not comfortable.”

With good reason. Republican challenger Mitt Romney continued to fight hard Monday, with five stops in four states and plans for two more events on Tuesday amid hope among his team and supporters that the energy at his rallies will translate into a big GOP turnout and a victory.

Obama’s campaign has spent enormous sums of money trying to make this election about Romney and a choice between competing visions. Those efforts took a toll on the challenger. But at heart, reelection campaigns are a judgment about the incumbent’s record in his first term and expectations about what a second might bring. Obama is not the same politician he was four years ago. If he wins, who would he be with another four years?

Would he become what he promised in 2008 but was not in his first term, a leader with the talents to guide a divided political system to a consensus on the country’s most intractable problems? Would the scars from a series of bitter fights with Republicans make him more or less inclined to make compromises he might have made in his first term? What would animate him in a second term? What would he pursue for his legacy?

He does not lack for ambitions. In a recent interview with editors of the Des Moines Register, an interview that initially was off the record, he expressed confidence that, as a newly reelected president, he could produce the grand bargain with congressional Republicans on a plan to deal with the federal deficit that he could not reach in the summer of 2011.

He said the bargain he seeks is one that would include $1 in new revenue for every $2.50 in spending cuts. It would not be easy to strike a deal with Republicans, he said. In fact, he acknowledged, it would be messy. But he said he thinks he could engineer a credible compromise.

A second priority, he told the Register, would be comprehensive immigration reform, something President George W. Bush, his predecessor, was denied because of opposition within his party. Obama said he is confident that he could get something done on the issue in a second term because he believes that if Republicans lose this presidential race, enough of them will conclude that they need to repair their relations with the Hispanic community.

What’s most interesting about what he told the Register is that these are things he rarely spoke about on the campaign trail. Obama, like Romney, has a five-point plan. His includes creating more jobs, particularly in manufacturing; developing domestic energy from all sources; putting more money into education and training; taking some of the money now spent on the war in Afghanistan and putting it into rebuilding the United States’ infrastructure.

He does mention dealing with the deficit, but he does not address it with the specificity or sense of urgency that the size of the problem requires. He talks about immigration even less, although his aides have long said it would be the priority the president said it would be when he was speaking off the record. But he has not truly sought a mandate for such an agenda.

The ambition to reach compromise on two issues that have divided Washington and the country for years speaks to what advisers say is his innate desire to find consensus around big and difficult issues. It is, they contend, part of Obama’s political DNA, and they believe he would be more committed to operating that way in a second term.

Republicans dispute that. They see an ideologically driven, big-government liberal whose ambitions all point left, and they think that a second term would bring more. But their credibility is low, given that they have tried to block Obama at virtually every turn and have shown no interest in compromising with him. The president’s advisers assume — hope — that a victory on Tuesday would lead to a new relationship with the opposition party, but it would be in Obama’s hands to bring it about.

That Obama is not the same candidate he was four years ago is evident from the campaign he has run. It has been hard-edged and negative. He spent as much time attacking his opponent as he has offering a hopeful vision. He spoke of his desire for cooperation, but it was tinged with suggestions that he has limits.

Is all this merely what he must do to win — what any politician would do faced with a difficult reelection and an energized opposition? Is it designed to reassure his supporters who fear that his backbone is not as strong as they would like?

In the closing days, Obama has capitalized on Hurricane Sandy to preach the importance of setting aside politics to work together. New Jersey Gov. Chris Christie (R), who has been one of the president’s harshest critics, has become Obama’s protector, offering praise for the way he has responded to the storm. The rest of the campaign — from Obama’s side and Romney’s — has served to divide the country even more.

Obama will soon learn whether he will be given another term. If he is, he will have a second chance to show what he is all about.