Editor's note: Julian Zelizer is a professor of history and public affairs at Princeton University. He is the author of "Jimmy Carter" and of the new book "Governing America."
(CNN) -- When Washington gets back to work, the situation will be difficult. President Obama won a sound re-election victory, doing very well in the Electoral College and winning the popular vote by more than 3 million votes. He trounced Mitt Romney in almost all the battleground states and he will return with a larger and more energized Senate majority.
Yet President Obama likely understands that elections don't remake the political system. The parties remain as polarized as ever, and the political process will be as difficult as it has been since the first day he took office. Republicans retained control of the House, where they can make it hard for the president to move his agenda forward and can place immense pressure on him to curtail spending.
While Democrats control the Senate, with 54 votes, Republicans control the tools of the Senate minority -- namely the filibuster, which requires 60 votes to pass any major piece of legislation. Exit polls showed that the public is not satisfied with the status quo, many voters opposed the idea of an activist government to solve problems, and President Obama struggled with some key constituencies, including older and suburban voters.
In general, second-term presidents, even those with landslide victories, have trouble with Congress (think of FDR after 1936), and President Obama must spend much of his political capital making sure that existing programs, like the Affordable Health Care Act, are implemented effectively.
Despite these challenges, political incentives for both parties could inspire legislative breakthroughs in several areas. President Obama does not have to remain content with the domestic agenda he has already achieved. He could succeed like Ronald Reagan in 1986, when Congress passed, with bipartisan support, a major tax reform bill that closed many loopholes and lowered rates.
In the short-term, deficit reduction offers the greatest potential for such a breakthrough. The process toward reducing the deficit will begin even if the president and Congress take no action.
The 2011 Deficit Control Act will require $100 billion in spending cuts starting in January. At the same time, the current income tax rates are set to expire on December 31, along with the Social Security payroll tax holiday. By making progress on a "grand bargain" over long-term deficit reduction, one that both parties could live with, President Obama could steal this issue away from the Republicans, positioning himself as the guardian of fiscal discipline just as President Clinton was able to do in the 1990s.
Now that Obama is freed from some of the political pressure from the left, whom he needed to mobilize voters for his re-election, he will have more room to maneuver. While Republicans don't want to hand the president any victories, they, too, would have incentives to agree so that they could show to their voters that they had delivered something big since taking over the House in 2010. On Wednesday, Speaker John Boehner indicated he would bend on raising revenue as part of the deal. The deal could include another tax reform measure, something that both parties have hinted at.
There are also policy issues that grow directly out of the election results. President Obama has been promising Latino voters that he would reform immigration policies. He has pledged to renew his push to pass the DREAM Act, a bill that has been stopped by Republicans, which would help almost 1.7 million young immigrants become citizens.
The huge Latino vote for the president, which played a critical role in battleground states like Colorado and Nevada, should bolster his resolve to take on this issue. And many Republicans will understand that the GOP's hard-line anti-immigration elements have become extraordinarily costly to the party. For more than a decade, those in the Republican Party who favor liberalized immigration policies, including George W. Bush and much of the business community, have been stymied by their colleagues.
Now, as Republicans look at the Electoral College math that led to Romney's defeat, there will be intensified pressure for them to change their anti-immigration reputation. "It's clear to me," Kansas Sen. Jerry Moran told Politico, "if Republicans are going to have the opportunity to be in the majority, we clearly have to determine how we deal with minority and Latino voters. In some fashion, the way we have dealt with immigration gives us a black eye."
Finally, there are long-term issues that might be on the radar as a result of crisis. The storms that have devastated sections of the country have given climate change more attention than ever. The impact on wealthier suburban communities has created more political support for addressing an issue that was largely ignored throughout the 2012 campaign. By producing legislation that deals with this grave problem, such as limits on domestic oil and gas drilling and more investments in solar and wind energy, each party could make progress toward solidifying support in key middle-class constituencies that are still struggling to dig out from the storms.
Nothing is inevitable in American politics. The history of Washington is filled with moments when something should have happened but didn't. Politics has a way of sidetracking progress on almost any issue. Talk about compromise that often follows an election is cheap, frequently leading to nothing.
The potential for some important breakthroughs, however, is there. The election's outcome gives both parties reasons to make deals with each other so they can each make gains with voters in 2014 and 2016. Sometimes, when politics and policy converge, progress in Washington is possible.
The opinions expressed in this commentary are solely those of Julian Zelizer.