How can the Republican Party — or the center-right political movement in this country generally — dig itself out of the hole it’s in? That’s the question being asked after two months in which the Republican Party lost a presidential election, had its positions on climate change and gun control challenged by the dominant press interpretations of Hurricane Sandy and the Newtown school massacre, and failed, at least so far, to use its control of the House of Representatives to avert the scheduled expiration of the Bush tax cuts.

Newt Gingrich, the former Speaker of the House who as a congressman engineered a Republican House majority, is out with a 25-point memo to the chairman of the Republican National Committee. Mr. Gingrich says the Republicans need to become competitive in California, in “urban America,” among blacks, Latinos, and Asian-Americans, among women, and “especially among younger single women.” He also calls for increasing Republican strength in what he calls “story telling and narrative development,” to challenge the left’s domination of “Hollywood, New York City, academics, the news media.” He asks, “how do we write off New England, New York, California, Illinois, etc. and think we are going to compete?”

Thomas Friedman, the author and journalist, calls for Republicans to launch an effort similar to what the Democratic Leadership Council did with the post-Carter, post-McGovern Democrats. He writes that the Republicans need to return to the “center-right” from the “far right.” The center-right, in Mr. Friedman’s view, would raise taxes on millionaires, support an assault weapons ban, and ratify the U.N. Convention on the Rights of People With Disabilities. He doesn’t really explain much how that center-right party would be different from the Democrats. Nor does he deal with the fact that the past two Republican presidential nominees, John McCain and Mitt Romney, were both in some significant ways center-right figures. They lost. So, too, were Bob Dole, who was the nominee in 1996 and lost, and George H.W. Bush, who lost his bid for re-election in 1992.

Peggy Noonan, the speechwriter for President Reagan and columnist for the Wall Street Journal, recommends an essay by James Kurth, a senior fellow at the Foreign Policy Research Institute. It says Republican prospects will be bleak unless the party can peel away white women from the Democrats.

The next generation of Republican leaders and possible presidential candidates — Paul Ryan, Marco Rubio, Chris Christie, Ted Cruz, Nikki Haley, Bobby Jindal, Scott Walker — will have to sort out these issues.

It’s worth remembering, too, that there was a prior generation of Republican leaders who won in states and demographics that are traditionally Democratic. Governors such as Pete Wilson in California, William Weld in Massachusetts, and George Pataki in New York managed to win the support of what Mitt Romney might have called “binders full” of women. They were environmentalists, they strayed from Republican orthodoxy on abortion rights, they were supporters of legal immigration. They were conservatives on taxes and spending, and they were tough on crime, at least in comparison to the Democrats they were running against.

Neither Wilson, Weld, nor Pataki were ever really fully embraced by the national Republican Party, though Mr. Pataki had a prominent speaking role at the 2004 Republican National Convention in New York, as did Arnold Schwarzenegger of California, another governor in the Wilson-Weld-Pataki mold. They were sometimes denounced as RINOS, or “Republicans in Name Only.” Rudolph Giuliani, the former mayor of New York, who has a similar profile, made an unsuccessful run at the presidency in 2008.

Mitt Romney was like this group in that he was a governor from a traditionally Democratic state who had once supported abortion rights and taken a hard line against pollution, but by the time he made it through the Republican primary and the wave of Democratic negative advertising, there wasn’t much of that profile left to emphasize for the general election campaign.

The natural move for the Paul Ryans and Marco Rubios of the world is to spend a lot of time courting Republican leaders in Iowa, New Hampshire, and South Carolina, while trying to anticipate whatever the issues are going to be in 2016. But looking past the nomination battle to the general election, the smart choice for anyone who wants to lead the GOP out of the wilderness would be to take some meetings with Governors Wilson, Weld, and Pataki.

The 1990s, when all three men were first elected governor, may seem like ancient history at this point. But one of the ironies of American politics at the moment is that it may be three old white men who never were elected president — Governors Wilson, Weld, and Pataki — who can tell the Republicans how to broaden their appeal enough to retake the White House.

Mr. Stoll is editor of FutureOfCapitalism.com.