Now that President Obama’s inauguration is behind us, the new Congress has been sworn in, and Punxsutawney Phil has predicted an early spring, we have entered a period of GOP soul-searching.

Republicans have embarked upon what Politico.com describes as a very public “colonoscopy” — an aggressive search for answers to why the GOP lost in 2012. And for someone to blame.

Many Tea Party activists and conservative talk radio hosts have lashed out against the “establishment” for coalescing around “wishy-washy moderates.” They argue that, next time around, the GOP needs principled conservative candidates like newly elected Texas Sen. Ted Cruz. Even some Massachusetts Republicans say they are “glad” Scott Brown bowed out of another Senate run. “Maybe now we can get someone who’s actually conservative,” they whisper.

Other Republicans have reached the exact opposite conclusion: that the GOP needs to become more moderate.

Speaking Wednesday at a panel on “The Future of the Republican Party” at Harvard, Republican consultant Ana Navarro argued that GOP intolerance of social and environmental liberals has alienated younger voters. And former Massachusetts Lt. Gov. Kerry Healey made the case for welcoming libertarian voters into the Republican fold.

Who is correct? Does the Republican path to victory veer left or right?

The answer is both — and neither.

Mitt Romney did not lose the presidency because he was a “Massachusetts moderate.” Nor did he lose because of conservative positions on social issues.

Romney lost because average voters simply could not relate to him and — rightly or wrongly — believed that he was unable to relate to them.

Likewise, Scott Brown didn’t lose the Senate race because he is too liberal for Massachusetts. Nor did he lose because the national party is too far right. Brown lost for one simple reason: President Obama had long coattails.

So, what does this mean for the future?

That depends, in part, on where you live. Says John Murray, a Republican strategist and participant in the Harvard panel, “A Republican in Massachusetts isn’t going to look like a Republican in North Carolina, and that’s the way it should be.”

This notion — that different states will elect representatives from different wings of the party, and that the national party should impose no litmus tests — is, at its core, deeply Republican. On matters of policy, the GOP rejects top-down solutions imposed by Washington bureaucrats. Why should our approach to party-building be any different?

As much as I’d love to see Massachusetts elect a U.S. senator who shares my conservative values, I understand that it’s not going to happen. And so, to borrow a phrase from William F. Buckley, I support the most conservative candidate who can win … in Massachusetts.

As for national politics, Republicans would be wise to learn from the man whose 102d birthday was last week. The political genius of Ronald Reagan was not that he imposed ideological purity upon a compliant party, but rather, that he cobbled together a coalition of social conservatives, fiscal conservatives, and foreign policy hawks with little in common other than their support for Reagan.

The lesson of the past two presidential election cycles is this: it is the likeability of the candidate at the top of the ticket that matters most.

What Republicans need, then, is not some ideological purge, but a presidential candidate who can relate to regular people. That person is out there. So, let Democrats delight in watching the GOP’s public autopsy. But Dems would be wise to remember that, like the groundhog’s prediction of an early spring, reports of Republican demise are really just some people’s wishful thinking.