President Obama and Congress proved during the lame-duck session that they can work together to resolve big and thorny issues, but that remarkable show of bipartisanship in all likelihood will be short-lived.

The Democrats don’t own the House anymore, and their Senate majority is smaller. In securing the $858 billion tax-cut and unemployment-benefit package, Mr. Obama cashed in his one big bargaining chip with the Republicans: allowing the Bush-era tax cuts to continue even for the wealthiest taxpayers. He also infuriated his liberal base.

“He doesn’t have much to bargain with come January,” says historian Julian Zelizer, at Princeton University.

Caught between an empowered right and a balky left, Obama appears to be in a bit of a box. But predictions of total gridlock in the 112th Congress may be premature. In fact, analysts say, Obama and the Republicans both need to accomplish two things: show they can govern while also drawing lines in the sand. So over time, expect a combination of collaboration and conflict. Obama can also avoid Congress altogether, changing policy by executive order and using the bully pulpit to try to shape public opinion.

That message, he said, was: “It’s time to find common ground on challenges facing our country. That’s a message that I will take to heart in the new year, and I hope my Democratic and Republican friends will do the same.” Obama already appears to have been rewarded by the public for reaching across the aisle. Even if most Americans weren’t happy that the Bush-era tax cuts were extended for the wealthiest taxpayers, they liked the bipartisan dealmaking.

“This is not lost on him,” says Bruce Buchanan, a presidential scholar at the University of Texas, Austin.

A Gallup poll released Dec. 23 showed Obama’s approval rating rose nine points in the previous two weeks among centrist Republicans and independents who lean Republican, hitting 29 percent.

At the same time, analysts warn, Obama has to be careful about alienating his progressive Democratic base.

“The outlook he’s taken is he doesn’t [have to worry about liberals], and what’s more important is moderate voters, and the left will come out for him when they see the choice in 2012,” says Mr. Zelizer of Princeton. “But that’s a dangerous posture to take. He needs the Democrats in Congress to protect health-care reform and at least try to move the legislation he gives them. He needs Democrats to make the case for why he should be reelected.”