WASHINGTON — When Republican leaders in Congress agreed to raise taxes on the wealthy last week, it left the increasingly fractured and feuding party unified on perhaps only one point: that it is at a major crossroads.
From Mitt Romney’s loss on Election Day through the recent tax fight that shattered party discipline in the House of Representatives, Republicans have seen the foundations of their political strategy called into question, stirring a newly urgent debate about how to reshape and redefine their party.
At issue immediately is whether that can be achieved through a shift in tactics and tone, or will instead require a deeper rethinking of the party’s longtime positions on bedrock issues like guns and immigration.
President Obama intends to test the willingness of Republicans to bend on those issues in the first months of his new term, when he plans to push for stricter gun control and a comprehensive immigration overhaul.
The coming legislative battles are certain to expose even more division in the party. And with establishment Republicans and Tea Party activists at times speaking as if they are from different parties altogether, concern is spreading throughout the ranks that things could get worse before they get better.
‘‘The Republican Party can’t stay exactly where it is and stick its head in the sand and ignore the fact that the country is changing,’’ said Ralph Reed, the founder of the Faith and Freedom Coalition and onetime leader of the Christian Coalition. ‘‘On the other hand, if the party were to retreat on core, pro-family stands and its positions on fiscal responsibility and taxes, it could very quickly find itself without a strong demographic support base.’’
Having lost the popular vote in five of the last six presidential elections, Republicans now face a country that is increasingly younger, multiethnic, and skeptical of Republican positions on some social issues.
The party’s deficit-cutting agenda relies heavily on reducing taxes for the wealthy, which irks middle-class voters, and cutting spending on government programs, like Social Security and Medicare, that are popular with many voters.
Generational change is also robbing the party of some of its most effective political positions. Same-sex marriage, which less than a decade ago was an issue that reliably drove conservative voters to the polls in favor of Republicans, appears to be losing its potency with an electorate increasingly comfortable with gay unions.
None other than Newt Gingrich, a former House speaker who promised to fight for a constitutional ban against same-sex marriage during the Republican presidential primaries, now says his party must come to terms with the country’s rapidly shifting views on the subject.
“Walking around and pretending it doesn’t exist just means you’re going to become irrelevant,’’ Gingrich said in an interview.
Prominent Republicans insist that if the party’s disparate factions can come together around a set of economic, social, and foreign policy principles in the coming years, they stand a good chance of retaking the presidency, making gains in Congress and repairing some of the damage done through several years of bitter primary battles and divisive legislative bickering.
“Republicans will get their mojo back when they define themselves as the party of economic growth and upward mobility,’’ said Governor Mitch Daniels of Indiana, a Republican who will become the president of Purdue University next week. Daniels said new lawmakers and governors — many of whom are minorities and women — would reshape the Republican Party.
‘‘The party, with all its problems — and I’m not disputing them — has a really large and interesting crop of new faces,’’ he said. ‘‘Ultimately, parties tend to be defined by their most visible personalities.’’
Republicans have already demonstrated success in midterm elections, when fewer people vote, and in state elections for governorships and legislatures. In North Carolina, Pat McCrory, a Republican former mayor of Charlotte, was sworn in as governor Saturday after waging a campaign that emphasized pragmatism over ideology.
‘‘My message remained a Republican message,’’ McCrory said, suggesting that national Republicans could learn a lesson from state politicians. ‘‘But I did it with a tone of problem solving. I did it with a tone of cooperation. I didn’t run one negative ad.’’
But a changed tone alone may not do enough to smooth over the very real disagreements in the Republican Party. And it is not clear how the intraparty combatants can meet in the middle. For example, while some Republicans argued that the tax vote last week enshrined almost all of the Bush-era tax cuts into permanent law and should be seen as a victory, harder-line fiscal conservatives called it a shameful departure from the party’s two decades of successful opposition to tax increases.
Clashes between Tea Party supporters in the House and Speaker John A. Boehner during the budget battles last year led a dozen of them to withhold their votes for speaker last week.
And across the country, deeply conservative organizations angry about the concession on tax increases are pledging more, not fewer, primary challenges to Republicans they believe are straying too far from the party’s orthodoxy on taxes, guns, energy, immigration, spending, and abortion.
“The gloves are off,’’ said Everett Wilkinson, a founder of the Tea Party movement in Florida. ‘‘We’re going to challenge a lot of the GOP going forward,’’ he added, both in primaries and general elections.
Moderate Republicans are bracing for the challenges. Steven C. LaTourette, who retired from his Ohio congressional seat at the end of the year and will become the president of the Republican Main Street Partnership, said his group would raise money to defend middle-of-the-road Republicans against the more conservative groups.