As they prepare to settle in for another four years of President Barack Obama, Republicans are already busily working on their roadmap to retake the levers of power in Washington. Whether they will need a modest re-calibration or a wholesale reinvention remains an open question.

Obama's November victory arguably marked a new low point for the GOP. The Republican Party now wrestles with a president unburdened with the stresses of an impending re-election campaign and enjoying relatively high popularity.

What’s more, Obama has already worked to set in motion an aggressive – and mostly progressive – agenda that makes most conservatives cringe.

For Republicans, the work to re-position themselves to win back the White House in 2016, and, before that, shore up majorities in the House and Senate, has already begun. And a key step toward reaching those goals, said Republican National Committee Chairman Reince Priebus, involves making the party more inviting to voters who do not traditionally compose the party’s base.

Jason Reed / Reuters Republican National Committee Chairman Reince Priebus gavels the 2012 Republican National Convention into session during the opening session of the Republican National Convention in Tampa, Florida August 27, 2012.

“We didn’t lose Wisconsin because we weren’t Facebooking pheasant hunters,” he said. “We need more voters.”

Democrats’ victories prompted a round of hand-wringing and recrimination in the immediate aftermath of the election. Having been drubbed among women and Latino voters, some Republicans argued for finally embracing some sort of immigration reform, and directed their ire toward those high-profile Republican candidates who made controversial comments about abortion and rape that fall. Still others pointed to the Obama campaign’s decisive advantage over Romney in digital outreach and voter targeting, while others laid the blame for the party’s defeat squarely with Romney himself.

“This certainly isn't the first time a party loses a presidential election and has to figure out how it does better,” said Henry Barbour, a Republican National Committee member from Mississippi who’s helping to lead the “Growth and Opportunity Project,” the RNC-commissioned review of the party’s failings in the 2012 elections. “Things are never as good as you think, or as bad as you think.”

Some of the project’s recommendations, which are on course for release as soon as March, are glaringly obvious. Republicans are virtually unanimous in agreeing on improved digital tools to court voters, as well as improved outreach to key voting communities – like Hispanics or women voters.

Priebus said he’s taking a cue from former Vermont Gov. Howard Dean’s “50 State Strategy” he enacted as chairman of the Democratic National Committee.

“We have to compete everywhere again. You go back and look at the electoral map in 1988, and you look at the states that were red. It’s stunning,” he said. “I think the charge for us is to run up the hill and make the case everywhere that the Republican Party is the home for more Americans.”

'Battle over strategy'

But as party leaders fan out to hear from elected officials and grassroots activists alike about the trajectory of the party, the GOP on Capitol Hill has been anything but a tribute to party unity.

If House Speaker John Boehner’s remarks about accepting new revenue in the aftermath of Obama’s victory were emblematic of Republicans’ soul-searching after the election, then the weeks since then have painted a vivid portrait of just how divided the GOP is about its path forward.

“If we’re split on anything, it’s on strategy, not the final goals,” said Rep. Mick Mulvaney, R-S.C., a darling of conservatives. “I think what you’re seeing now is a battle over strategy, not over principle.”

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The battle over the so-called fiscal cliff laid bare many of the fissures that plagued Republicans in Congress for the past two years, bringing the government to the brink of shutdown several times and almost tipping the government into a default on its debt. The party’s ability to speak with one voice has been hampered by familiar internal, ideological divisions.

When Boehner offered to raise taxes on millionaires – a concession, but one that Obama dismissed outright – conservatives undercut their leader’s bargaining position by refusing to pass it out of the House.

Even when Democrats won an income tax hike, it was over the objections of most House Republicans; Boehner won another term as speaker over the defections of some high-profile conservatives, including Mulvaney, who did not vote.

“I do believe that, as a party, we need to focus on the things that unite us,” Barbour said. “Folks in the party aren't going to agree on everything, and that's OK. The Republican Party is a diverse, broad party.”

And as party leaders attempt to put a fresh face on the Grand Old Party, the first few months of Obama’s second term seem destined to test the divisions among Republicans.

The president has signaled his intention to seek comprehensive immigration reform and new, stricter controls on firearms – two initiatives that could split conservatives who want to hold the ideological line from Republicans who wish to shed the party’s image of intractability, and cut some sort of a deal with Obama.

Those battles will play out alongside what’s expected to be a bruising fight in just a few weeks over raising the debt ceiling, continuing government spending and dealing with the automatic spending cuts in the fiscal cliff, which were delayed for two months past the beginning of this year. The deadlines for all three of those issues fall within a few weeks of each other in late February and early March.

'We have a mish-mash'

And already, some Republicans are openly discussing the possibility of a shutdown or default, things which Boehner and other GOP leaders had openly disavowed during similar fights in 2011. Mulvaney said “the world is not going to end” if the U.S. defaults on its debt.

“No one wants to default; not even the most right-wing nutjob wants to default,” he said. “But do we want to throw money at paying the light bill at the Department of Education?”

But as Republicans wrestle with these divisions, there’s always the hope of the one development that seems to solve most problems in politics: winning.

After Romney’s loss and Boehner’s struggles with his rank-and-file, Republicans lack for any natural leader behind whom the party could rally. The country is still years away from the next presidential primary, a contest which might test many of these same fault lines within the GOP.

“It's absolutely a challenge that we face. The Democrats have Barack Obama, and we have a mish-mash,” Mulvaney said. “We have the speaker of the House, the minority leader of the Senate, various outside groups and very vocal folks over in the Senate, along with a cast of presidential cast-offs in the last four years. We haven't really coalesced yet.”

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