President Barack Obama left Washington on a high last month after racking up victories in the lame-duck session. But he returns this week to a much different climate: His own party is deeply divided over how he should work with the new Congress and Republicans are ready to hold him to his word about cutting deals together.

Rep. Jerrold Nadler, a vocal member of the Congressional Progressive Caucus, said Obama should take “exactly the opposite” stance of a bipartisan broker, even though Republicans now control the House and have six more Senate seats.

“This mania about cutting the budget while cutting taxes is absurd,” said the New York Democrat, who urged Obama to stay focused on job creation instead of bowing to GOP demands to slash government funding.

“It would be a major mistake to be bipartisan with people who aren’t going to be bipartisan. You’ve got to be willing to draw lines in the sand and educate the public,” Nadler said.

But Rep. Henry Cuellar, a member of the fiscally conservative Blue Dog Coalition, said the president should only stand firm on certain issues given the reality that Republicans hold more sway in Congress.

“He needs to push back a lot more” on Republican efforts to repeal health care reform and block judicial nominations, the Texas Democrat said. But when there are areas where “he can reach out, triangulate or whatever, he definitely needs to take a closer look.”

Republicans are keeping a running list of issues that they want Obama to help them advance. Incoming House Majority Leader Eric Cantor (Va.) said he will be looking to Obama to work with the GOP in areas they have both identified as being ripe for bipartisan progress: cutting spending, earmark reform, tax reform and scaling back regulations on businesses.

“I expect this president to put some action behind the words that he has been using,” Cantor said during a sit-down with reporters. “I hope that he picks up the phone and calls [Senate Majority Leader Harry] Reid … and insists that he join us in making sure that there are no earmarks in legislation coming out of Congress.”

Obama, who returned to Washington on Tuesday after spending the holidays in Hawaii, oversaw passage of an impressive number of issues in the final days of the lame-duck Congress, including the ratification of the Strategic Arms Reduction Treaty and the repeal of the military’s “don’t ask, don’t tell” policy, a major victory for his base. Moreover, Obama said the lame-duck session should be a model for how the new Congress can succeed.

“If there’s any lesson to draw from these past few weeks, it’s that we are not doomed to endless gridlock. We’ve shown, in the wake of the November elections, that we have the capacity not only to make progress, but to make progress together,” he said at a news conference just before leaving for Hawaii.

But he is already signaling that he knows of the delicate balancing act in store for him in the months ahead.

“There’s going to be politics. That’s what happens in Washington. [Republicans] are going to play to their base for a certain period of time,” Obama told reporters aboard Air Force One on Tuesday.

“My expectation, my hope, is that [Speaker-designate] John Boehner and [Senate Minority Leader] Mitch McConnell will realize that there will be plenty of time to campaign for 2012 in 2012,” he said. “Our job this year is to make sure that we build on the recovery. We started to make good progress on that during the lame duck, and I expect to build on that progress when I get back.”

A McConnell aide said Republicans have already shown they are willing to work with Obama on areas where they share common ground — even when Democrats won’t.

“McConnell has said that if the president wants to do things that we’ve been calling for, why wouldn’t we want to work with him? See the tax bill, for example. It wasn’t Reid and Pelosi on that stage,” the aide said, referring to the fact that neither Democratic leader attended last month’s signing ceremony for the tax cut package.

But senior Democratic aides cautioned Obama against losing sight of his base as he recalibrates his relationship with Republicans.

Many Democrats want to see the president “stand up and assert himself a bit more, especially since they think he got rolled in the tax cut debate,” one top House Democratic aide said.

Another senior Democratic aide said it is crucial for Obama to focus on the economy and on navigating budget battles, in addition to “positioning Democrats as common-sense leaders without abandoning basic Democratic principles.”

House Minority Leader Steny Hoyer said Tuesday that he hopes the president will continue to press for bipartisanship but, in the same breath, criticized Republicans for not working with Obama in the spirit that Democrats worked with President Ronald Reagan.

“You know, Social Security and tax reform under Ronald Reagan, it was an overwhelming Democratic House. We cooperated with the president. People tend to forget that,” the Maryland Democrat said. “This Republican Congress did not cooperate with Obama.”