There's no consensus yet on how to do it. With the next election three years away, Republicans are tiptoeing around policy changes even as they size up potential candidates who range from tea party heroes to pragmatic governors in Republican- and Democratic-leaning states.
There's a partial road map, but it's more than two decades old, and the other party drafted it. Democrats, sick of losing elections and being tagged as out-of-touch liberals, moved their party toward the center and rallied behind Arkansas Gov. Bill Clinton in 1992.
Strategists in both parties say Clinton's achievement, however impressive, may look modest compared to what a Republican leader must do to construct a new winning formula, given the nation's changing demographics.
"Our challenge was to get voters back," said Al From, a chief architect of Clinton's political rise. "Their challenge is harder: get voters to come into a new coalition."
That will be complicated, From said, because the Republicans' conservative base "is more demanding and more important" than the Democrats' liberal base.
An array of Republican campaign veterans agree. They say the party's loyal base of conservative activists — including evangelical Christians, anti-tax crusaders and anti-abortion advocates — is too big, ideological and vital to be treated with anything but great care and respect. Republicans will go nowhere if they lose a hard-core conservative every time they pick up a new unaligned voter with a more moderate message.
While they circle that conundrum, Republican leaders hope for a charismatic nominee in the mold of Clinton or Ronald Reagan. They yearn for someone who can appeal to less ideological voters without prompting conservatives to feel their principles are losing primacy.
Several veteran strategists say Republicans should focus less on modifying their ideas than on improving their campaign mechanics and finding nominees with broader personal appeal than Mitt Romney, John McCain and Bob Dole.
"The foundation of the party as a conservative party hasn't been the principal liability, but the principal asset," said GOP campaign strategist Terry Holt.
"Among every voter group there are people who share our values," Holt said. The key to winning, he said, is to perform better at "micro-targeting" and other techniques designed to find and motivate potential voters.
In that area, he said, "the other party is about half a light year ahead of us."
Arizona-based Republican consultant Eddie Mahe said finding a charismatic candidate is more important than tweaking policies. Given Americans' low opinion of politics, he said, "to sell the party as a party is nonsensical."
Instead, Mahe said, Republicans must pick a nominee who appeals "to the non-voters, disinterested voters, the uninformed — whatever you want to call them — who are attracted to a personality, someone they feel good about."
The Republican who comes closest to that description, he said, is Rep. Michele Bachmann of Minnesota, a tea party favorite. But Mahe said he doubts she could win a general election.
Dan Schnur, a former aide to President George W. Bush who teaches political science at the University of Southern California, said: "Parties don't remake parties. Leaders remake parties."
Schnur agrees that Clinton was a gifted politician, but he also had some help and luck, which Republicans will need, too.
Clinton has acknowledged that Gary Hart began tugging the Democratic Party from its liberal and outdated moorings in 1984 and 1988, even if he eventually fell short of the nominations. And a 1992 candidacy by New York governor and liberal hero Mario Cuomo might have doomed Clinton's lean-to-the-center strategy.
Republicans "need a Gary Hart before they get a Bill Clinton," Schnur said. And they may have trouble narrowing the ideological field in the 2016 primary and beyond, which could force the eventual nominee to embrace hard-right principles that excite GOP activists but turn off independent voters.
A 97-page post-mortem, commissioned by the Republican Party after Romney's loss last fall, said the GOP "is increasingly marginalizing itself, and unless changes are made, it will be increasingly difficult for Republicans to win another presidential election in the near future."
The report emphasized messaging and outreach more than possible changes to policies and proposals. "The party should be proud of its conservative principles," the report said, but it also must be more "welcoming and inclusive" to young voters, minorities and women.
From — who founded the Democratic Leadership Council, a key proponent of Clinton's 1992 agenda — says Republicans are on the wrong track. They must be more open to adjusting their policies, he said, if they want to win presidential elections.
In the early 1990s, From said, "people didn't trust Democrats on the economy, national security, crime, welfare." By pushing welfare reductions, community policing and other new ideas, he said, "we tried to systematically eliminate the obstacles. Republicans have got to do the same thing."
Clinton's 1992 team believed "if you get the argument right, people will vote for us," From said. "Republicans don't have the argument right."
Clinton campaign aide Paul Begala said parties that win presidential elections are "always more mainstream and more unified. Right now, the Republicans are neither."
Begala said liberal activists made only modest complaints about Clinton's shift toward the political center because they were sick of losing elections with nominees such as George McGovern, Walter Mondale and Michael Dukakis.
He said Republicans might need one more presidential loss to create a similar level of frustration, which can open the way to pragmatism and moderation. Nominating a tea party-leaning "true believer" such as Sen. Ted Cruz of Texas could do the trick, Begala said.
Holt, who has advised numerous GOP campaigns, said Republicans have already learned the lesson. "The most effective remedy for any party is an overdose of defeat," he said. "We've suffered that."
The Republicans' challenge is spelled out in exit polls from President Barack Obama's win over Romney. Nearly two-thirds of Republican voters labeled themselves as conservatives. But fewer than half of all Democratic voters called themselves liberals.
That indicates Democrats are working with a less ideological, more flexible base, giving a nominee leeway to embrace issues that might attract non-aligned voters in the general election.
Republicans, on the other hand, depend on a more ideological base. That's one reason party leaders — for now, anyway — talk less of modifying party policies and more of changing mechanics, technology and messaging.
"The brand has suffered," Holt said, "but the values have been very consistent."