Beyond the fiscal issues, immigration, as The New Yorker‘s Ryan Lizza wrote in recent piece, may be the most obvious issue of compromise between the two parties, in part because of politics. If Obama wins reelection, it will in part because he runs up a huge margin over Romney among Hispanic voters.

Related: Obama pushes for immigration reform

Republicans, seeing demographic trends headed against them, may be willing to adopt a Dream Act-style bill that prevents the deportation of the children of undocumented immigrants, formalizing what Obama has done through his enforcement power as president. And they could even agree to some resolution for the more than 10 million undocumented immigrants living in the U.S.

White House aides acknowledge immigration is a big second-term issue, and the president has said as much himself.

“I can promise that I will try to do it in the first year of my second term,” Obama told Univision earlier this year, referring to immigration reform.

On energy, Bernstein was not sure a broad-based “cap and trade” plan that would tax carbon emissions could pass soon, but he suggested the two parties could reach agreement on other energy issues, like greater development of natural gas.

Democratic activists have a long list of other goals for Obama, many of which may be far out of his control: ending the “Drug War” and changing how drug crimes are prosecuted, appointing the first black female Supreme Court justice, and reducing the influence of money in politics.

And on many issues, Obama would face many of the same challenges in the second term that he has the last two years. Even if the jobless rate remains high, it’s unlikely Republicans in Congress or even some conservative Democrats will approve any kind of stimulus-style legislation that would send money to the states and help them stave off layoffs of teachers and other public sector workers. Targeted investments to reduce black unemployment, as many African-American leaders have urged, are very unlikely to be approved.

Republicans are also unlikely to agree to large spending increases to make it easier for young people to afford college, something Obama speaks frequently about.

Obama’s second term would also involve resolving key questions on healthcare, financial regulations and foreign affairs. He has already effectively ended U.S. involvement in Iraq, and if reelected, his administration would complete a drawdown of U.S. troops in Afghanistan.

Much of the healthcare law remains to be implemented. In particular, Obama and his team must reach an agreement with Republican governors, like Rick Perry of Texas and Rick Scott of Florida, who have said they will balk at expanding Medicaid to most low-income people in the their states, as the healthcare law calls for. That expansion is scheduled to begin in 2014.

Related: Why Republican governors are likely to buckle on Medicaid

Lastly, the Dodd-Frank financial regulation law, intended to stop a market crash like that of 2008, is facing legal challenges from Republicans and congressional GOP attempts to cut off funding for parts of it. White House officials consider that law one of the most important achievements of the president’s tenure, and will aggressively defend it.

Follow Perry Bacon Jr. on Twitter at @perrybaconjr