“In a second term,” Mitt Romney darkly warned members of the National Rifle Association last month, President Obama “would be unrestrained by the demands of reelection.”

But Romney was cagey about what, exactly, that would mean: His only specific prediction was that Obama would “remake” the Supreme Court. So it was helpful when, at the White House Correspondents’ Association Dinner a week ago, the president opened up about the “secret agenda” he has planned. “In my first term,” he joked, “we ended the war in Iraq; in my second term, I will win the war on Christmas. . . . In my first term, we passed health-care reform; in my second term, I guess I’ll pass it again.”

(Andrew Harrer/Bloomberg)

In other speeches, Obama has offered a more serious preview of what he’d like to get done if he’s reelected. On March 30, he listed second-term priorities including reforming the immigration system; remaking the nation’s energy policy so it addresses “the long-term challenges. . . . of energy independence and climate change;” doing more to ensure that “people who don’t have work can find work” and that “our housing system is working for everybody;” pushing forward on education reform; and executing an “effective transition out of Afghanistan.”

But that’s not really a list of what Obama will do in his second term. It’s a list of what he would like to do.

The president’s advisers are naturally reluctant to discuss what happens if their candidate wins in November. They don’t want to appear overconfident or undercut the messages of the campaign. None was willing to speak on the record. But in dozens of conversations over the past few months, it has become clear that their thinking on what the president can do has evolved significantly in the last four years.

In 2008, the Obama campaign often seemed to believe that as president, Obama would be able to personally inaugurate a new era of cooperation in Washington. But after the past three years, which have been full of debt-ceiling showdowns they didn’t want and jobs bills they couldn’t pass, they have become more realistic, and are quick to caution that, in most cases, what they can get done in a second term will depend on what Congress is willing to do with them.

The budget

Everyone from Obama’s closest advisers to the GOP’s top tacticians agrees that the first year of a second term — and perhaps even more than that — would be “fiscal.” That is to say, it would be devoted to budget and tax issues.

At the end of 2012, we’ll face what Federal Reserve Chairman Ben Bernanke calls “the fiscal cliff”: The Bush tax cuts are set to expire, the $1.2 trillion in automatic spending cuts initiated when the deficit “supercommittee” failed to reach a deal are set to begin, we’re expected to hit the debt ceiling again, and many other programs and tax credits will come up for renewal.

Around the Hill, they refer to this as “taxmageddon.” And it won’t wait for a second Obama term to officially begin: Most of it will come due in the lame-duck session. But everyone expects that the outgoing Congress will manage to kick the problem to the incoming Congress.

What no one knows, however, is what that next Congress will be like. Odds are that even if Obama wins, Republicans will hold the House and potentially win back the Senate. But after losing the presidency — after failing to achieve what Senate Minority Leader Mitch McConnell (Ky.) called their “top political priority” — would they be more or less willing to work with a man they couldn’t persuade the American people to fire?

“After you lose, there’s a circular firing squad that occurs,” says a former senior aide to the Senate Republican leadership. “You’ll have a wing of the party standing up and saying we did not adhere to our values strictly enough. And you’ll have a wing saying we did not appeal to independents.”

In a scenario where Republicans are willing to work with Obama — where they would accept $1 trillion or more in new revenue in return for cuts to entitlement programs — the president’s team can imagine getting quite a lot done, in part because there’s a lot that both sides want to do.

Both sides are aching to do tax reform, for instance. Both sides want an intelligent set of spending cuts. And both sides are seeking changes to entitlement programs such as Social Security and Medicare.

But agreeing on goals isn’t the same as agreeing on the policies needed to achieve those goals. Sure, both sides want tax reform, but they disagree on whether it should raise new revenue. And both sides want to replace the supercommittee’s automatic spending cuts, but Republicans want to substitute deeper reductions to domestic programs, and Democrats don’t. If these issues could be successfully navigated, however, that could build the necessary trust to take a run at entitlement reform.

It’s easier to see Democrats and Republicans coming together on a deal around Social Security than on Medicare and Medicaid. Bipartisan changes to the two health-care programs are complicated by the Affordable Care Act and GOP Rep. Paul Ryan’s budget, which have committed the parties to opposing visions for the health-care system.

But the two parties have largely left Social Security out of their arguments. Ryan’s budget leaves it alone. Obama’s plans do, too. The two sides haven’t polarized around irreconcilable ideas. It’s possible to imagine them going into a room and coming out with a deal. It could even be coupled with tax reform, since much of what needs to be done for Social Security relates to changing what and how it taxes.

Of course, if the post-election Republican Party pulls further to the right, then big deals are probably impossible. In that scenario, our fiscal problems might be solved when Congress fails to come to an agreement, and the Bush tax cuts expire and the spending cuts kick in. That would be devastating to the economy — I consulted some forecasters who thought we’d be in double-dip-recession territory — but it would cut the deficit in a hurry.

Climate change and immigration

Beyond the deficit, Obama’s advisers see two big unfinished pieces of business from the first term: climate change and immigration reform. Of these, it’s easier to imagine the president taking action on immigration reform, in large part because it’s easier to imagine Republicans coming to the conclusion that they need to support some version of immigration reform.

If Romney loses in part because he underperforms among Hispanic voters — recent polls have shown him in the teens and low 20s — pressure could build in the Republican Party to extend some kind of peace offering to Latino voters, with an eye toward 2016.

There’s less optimism when it comes to climate change. “I don’t think he can move a climate bill,” says Neera Tanden, president of the Center for American Progress and a former domestic policy adviser to Obama. That doesn’t mean, she says, that the president couldn’t move forward with a bill on renewable energy: “You can have an ‘all of the above’ strategy that really accelerates the effort to make us independent of foreign oil.”

Health care

On this issue, much of a second term would be devoted to consolidating the accomplishments of the first. Assuming that the Supreme Court doesn’t totally wipe out the Affordable Care Act, the law will begin covering uninsured Americans in 2014. But there’s an enormous amount of work to do to get ready for that date, and once the law goes into effect, there will be an enormous amount of work needed to iron out the kinks. If the court strikes down the individual mandate — which requires Americans to have health insurance or pay a fine — but leaves the rest of the legislation intact, that process becomes even more difficult and might require some kind of deal with Congress.

Either way, the administration is well aware that the health-care law, perhaps more than any other, is likely to be the president’s legacy, and they will attend to it accordingly.

Speaking of the Supreme Court, there will, of course, be nominations to worry about — vacancies are likely. In addition, Bernanke’s term is going to expire in 2014. If Obama were reelected, the administration would also have to replace a rush of outgoing staffers, likely to include Treasury Secretary Tim Geithner.

The Obama advisers I spoke with say that the White House expects the next Treasury secretary to be a point person in the fiscal negotiations. That argues for someone who knows the budget and knows how to work with Congress, such as Jack Lew, the White House chief of staff who previously led the Office of Management and Budget, or Erskine Bowles, who served as Bill Clinton’s chief of staff and who more recently co-chaired the Simpson-Bowles commission on deficit reduction.

Foreign policy

Presidents tend to have a freer hand on foreign policy, where Congress is generally less involved. So if Obama is facing a difficult Congress and he doesn’t have to spend his time campaigning for reelection, foreign policy is a natural place to put his energies — not to mention to burnish his legacy. Among his counselors, there’s a barely concealed sense of excitement about the possibilities in this arena.

As they see it, the Iraq war is officially over. The conflict in Afghanistan is winding down. Osama bin Laden is dead. The Obama administration, in other words, is nearer to a clean slate than they’ve been since taking office.

The next phase, in their view, would be focused on “rebalancing” America’s attention away from the Middle East and toward regions of the world that are more economically important to the United States.

As Secretary of State Hillary Rodham Clinton has said, that effort begins with China and the rest of the Asia-Pacific region. It could mean using free-trade agreements to increase our economic influence and the annual East Asia Summit to create an opportunity for multilateral engagement. Obama’s advisers would also like to spend more time building relationships with Brazil, India and Turkey.

Of course, they are quick to caution that Iran is the wild card. And just as the Sept. 11, 2001, attacks derailed the Bush administration’s plans, a major crisis, disaster or opportunity could decide the Obama administration’s second-term focus.