The new Congress offers new challenges for President Obama. He is asking House and Senate leaders to meet Friday at the White House.
It is their first chance to discuss what can get done in a capital that's even more divided than before, reports CBS News correspondent Bill Plante.
Both President Obama and Republican leaders say publicly that they want to find ways to compromise after the election. History shows it may be easier said than done, but the White House says progress will still be possible.
"The president is not going to let politics get in the way," press secretary Josh Earnest said.
Earnest suggested that President Obama may find common ground with Republicans on early childhood education and infrastructure investment
"Even if there are areas of disagreement on some issues, maybe there's an opportunity to compromise on some others," he said.
Mostly absent on the midterm campaign trail, President Obama took to the radio on election day acknowledging that many voters are frustrated.
"The polarization's gotten worse, obviously I have a strong opinion as to why that happened. But, you know, that does, that cynicism I think is something that we've got to fight against," Mr. Obama said.
The Republican leader in the Senate, Mitch McConnell, told CBS News he's optimistic.
"We do have an obligation to work together on issues where we can agree," McConnell said. "Just because we have a two-party system doesn't mean we have to be in perpetual conflict."
But history also shows compromise may be possible.
In 1988, President Ronald Reagan worked with a Democratic Congress to ratify a major treaty with the Soviet Union.
President Bill Clinton struck deals on welfare reform and deficit reduction after Republicans took control of both houses.
But President Obama faces greater odds. He plans to move forward with executive actions on immigration and climate change, despite Republican opposition.
"I think the final two years will be a period of expanded executive power... and I think in Congress, although there will be some talk of bipartisan cooperation, Republicans will be more focused on putting forward bills that set them up for 2016," presidential historian Julian Zelizer said.
There may be issues on which both parties see an advantage in compromise, but the president's staff has already issued veto threats on his behalf for many bills passed by the House which never got taken up when Democrats controlled the senate.
If those same bills come around again in the new Congress, there will likely be more clashes than compromise.