WASHINGTON - A top priority for Republicans as they take full control of Congress this week will be to repair their reputation as a divided party hobbled by infighting and permanent confrontation with President Obama.

The overarching ambition is to try to reshape policy in ways that prove to average Americans that Republicans can govern, especially with the 2016 presidential campaign in its early stages.

"I think a majority [of Republicans] recognize that we have to govern responsibly," said Sen. John McCain (R., Ariz.), who will become chairman of the Armed Services Committee. "We have to show that we can be a productive party, and that, I think, will have a direct effect on whether we're able to elect a Republican as president in 2016."

Incoming committee chairmen such as McCain are preparing fresh oversight of federal agencies while rank-and-file members will be encouraged to use a new budget plan and government spending bills to challenge the president by trying to roll back Obama's new environmental regulations, health-care reforms, and his outreach to Cuba and Iran.

But with public disgust at Washington at an all-time high, Republicans are even more eager to demonstrate that they can be productive and have some level of bipartisan cooperation with the president. Though, no one has bipartisanship as the top agenda item.

"On the things where we agree, the goal will be to make a law, not just put something on his desk," incoming Senate Majority Leader Mitch McConnell (R., Ky.) said in an interview, adding later: "I want to make it clear: Desire for a signature is not going to dictate everything that we do."

Securing final passage of bills will require McConnell and House Speaker John A. Boehner (R., Ohio) to compromise with Democrats while holding together their own ranks, who have clashed repeatedly over issues such as spending and immigration. Many GOP leaders hope that their differences can be set aside in favor of legislative wins.

The House and Senate formally reconvene on Tuesday. New members will be sworn in and top leaders and committee chairmen formally installed on a day steeped in tradition and ceremony.

Boehner and McConnell will be backed by larger GOP majorities: 246 Republicans in the House, the party's largest majority since just after World War II; and 54 GOP senators, an impressive gain but short of the 60 votes required to overcome most procedural hurdles Democrats will have at their disposal.

In the Senate, the rebranding effort will begin with energy policy.

McConnell plans to begin his tenure as Senate majority leader with a "full-throated" debate on national energy policy, ranging from a new oil pipeline to additional oil exploration. He has also promised consideration of liberal alternatives.

McConnell wants to use the controversial proposal to authorize construction of the Keystone XL pipeline as the genesis for a free-wheeling Senate debate about America's energy future, in which both sides will have the opportunity to offer and debate more expansive energy issues than just the narrow pipeline proposal.

"We can treat this like a serious and significant energy debate," McConnell said in a pre-Christmas interview in his Capitol office.

Obama has resisted GOP efforts to authorize the pipeline, but dozens of moderate congressional Democrats support the bill and a broader energy debate.

The open process is part of McConnell's effort to live up to his pledge to restore the Senate's grand tradition of free and full debate, while also advancing conservative causes. A skilled practitioner in the use of the Senate's arcane procedural rules to move or block legislation, McConnell has pledged to use those rules to score some conservative wins. He has been coaching GOP senators that their most likely path to wins will come on the annual spending bills for the federal government - which Republicans have routinely opposed on the grounds that they spend too much taxpayer money.

But now, with control of both houses, Republicans have more leeway to attach policy riders in the spending bills that will restrict federal agencies in their oversight of environmental, labor, and other regulations. These still may draw vetoes, but McConnell said he believes Republicans will have leverage to get some restrictions included, just as the mammoth spending measure approved last month included language sought by Wall Street firms making risky trades.

In the House, most of the early weeks will seem like a do-over of the last two years - except that many of the bills passed will get swifter Senate consideration.

Up first is a veterans employment bill that passed last year with bipartisan support, according to senior leadership aides. There's also a bill to loosen work requirements set by the Affordable Care Act and a similar bill to authorize the Keystone pipeline.

The second week of January will be devoted to a new spending plan for the Department of Homeland Security. The spending bill only funds the department until the end of February, a move designed to give Republicans more time to craft a legislative response to Obama's decision to change immigration policy through executive actions. But no specific proposals have yet emerged, the aides said.