WASHINGTON » Unpopular and divided, the once mighty House Republicans are laboring to repair their image and frame a new agenda.

Absent for now is a big, contentious docket similar to last year’s, which included the goal of writing new health care legislation to replace the Obama administration’s law. A long-promised overhaul of the tax code seems out of reach. When Majority Leader Eric Cantor, R-Va., issued a memo this week laying out the body’s initial legislative agenda, a centerpiece was a modest tax cut for small businesses.

With their poll numbers sinking and President Barack Obama attacking them — and poking fun in a weekend speech at the infighting among their leaders — House Republicans long to establish a reputation as the party of job creation and to blunt the notion that they are recalcitrant and combative.

Senior Republicans are eager to minimize the drama, letting the party’s presidential candidate, when he is finally chosen, take the lead.

"Most of us expect the major decisions aren’t going to be made this year," said Rep. Tom Cole of Oklahoma, a former chairman of the House Republican campaign committee. "It’s a very political year. The big thing for us is to not be part of the conversation instead of trying to inject ourselves into it."

But attracting positive attention while avoiding confrontation is proving to be a challenge in an election year, particularly for a group that in 2011 seemed to relish showdown after showdown.

Members are still struggling to sing from the same legislative hymnal. Many want to do bigger things, like a tax code overhaul and changes to the Medicare program. Others, including Cantor, knowing they will get no help from Senate Democrats, seem to favor more incremental steps.

Many of the more conservative members, particularly some freshmen, want to continue taking the good fight to Democrats.

"We should focus on standing for principle and put the politics aside," said Rep. Todd Akin of Missouri, who is in a Republican primary fight for a seat in the Senate. "You have to keep doing what you think is the right thing to do."

Others desperately want to find bipartisan compromises that can become law. "The system is designed to make things difficult," said Rep. John Campbell of California. "You just have to persevere. Agreements take time, and they’re supposed to."

Outside pressures from each end of the political spectrum, which have dogged the House all year, are myriad: a five-year transportation bill, a major priority of Speaker John A. Boehner, is being attacked by the left, for including new oil drilling as a way to pay for the bill, and the right — Heritage Action for America, a conservative group, is urging Republicans to reject new highway spending.

Further, Boehner and Cantor, whose strained relationship recalls the days of the intraparty intrigue that bedeviled Newt Gingrich as speaker, have had to spend time trying to stamp out perceptions that they are working at dangerous cross-purposes.

Their tensions are so well known that Obama joked about the two at a black-tie banquet Saturday night. ("Speaker Boehner, it is good to see you at the head table. I know how badly Eric Cantor wanted your seat.") Members grouse regularly about the seeming divisions, and Cantor’s staff felt it necessary this week to extensively explain that their two staffs had called a truce.

"As you’re clearly aware," Boehner said Thursday, "there have been some staff rumbles from time to time, but that’s to be expected when you’re doing big things. And members and our staffs, they’re passionate about what they do. Sometimes that leads to some disagreements."

Further, a tangle in December over extending the payroll tax cut pit House Republicans against Senate Republicans, who argue that their House colleagues need to settle down and find a uniform message with them.

"A body of 535 doesn’t sing easily in one chorus," said Sen. Lamar Alexander, R-Tenn. "I would get up in the morning, look in the mirror and say three words: ‘the Obama economy.’ Then say, ‘They’ve been in charge, they made it worse, we can make it better.’ And remember all three messages."

Defense is not a position that House Republicans of the 112th Congress are accustomed to playing. The group had remarkable leverage last year, setting the agenda on spending — reining it in beyond what even Boehner would have dreamed — and beating back Democrats on a variety of policy areas in the process.

But the public audience was not always wowed by their accomplishments. Polls showed that many Americans, even those who agreed with the Republican fiscal agenda, found the process, which included nearly shutting down the government, too messy. And among hard-core conservatives, the Republican gains were often too slight to win them applause.

At their retreat in January, Republicans tried to get back on the same page. They are now trying hard to demonstrate where they agree with Democrats, like in the area of small business, while still hammering away at Obama on unemployment and energy policy, subjects they think resonate with voters.

Should the Supreme Court find fault with some or all of the health care law, Republicans will be ready with a replacement, they say, and will push a bill banning stock trades by lawmakers and staff members with conflicts of financial interests.

House and Senate negotiators are locked in talks to extend the payroll tax cut through the rest of the year, as well as to extend unemployment compensation and stop a deep cut in payments to doctors treating Medicare patients.

"We’ve had a lot of positive discussions about the year ahead," said Kevin Smith, a spokesman for Boehner, "and our members are united against the president’s policies, which are making the economy worse, and united in our efforts to offer better solutions to help middle-class families and small businesses."

Further, House Democrats, for all their excitement over the other party’s missteps, have their own problems, including retirements by members in districts tilting Republican.

Small, for now, may be best, Republicans say. "We are worried about trying to produce a result, make incremental progress and find common ground here," said Brad Dayspring, a spokesman for Cantor. Time and time again, he said, "when you try to go big and grand and do grand bargain-type deals, it collapses of its own weight.

"When that happens over and over again," he continued, "what do you do? You try something new."

© 2012 The New York Times Company