The winds of moderation seem to be blowing through the Republican Party.

OK, maybe it’s just a breeze, and a gentle one at that. But after four years of stuck-in-cement opposition, the Party of No is sounding like the Beatles singing “We Can Work It Out.”

What a difference a White House walloping makes. Now even the party’s biggest stalwarts are saying the Republicans face demographic disaster unless they overhaul their image.

“It’s called the new reality,” former Republican chairman Michael Steele tells me. “We can no longer afford to marginalize ourselves as a party.” The GOP has gone “off the rails,” he says. “We are becoming increasingly irrelevant to the political conversation.”

If so, Republicans are trying to push their way back into that dialogue. Here’s Sen. John McCain on abortion, telling Fox News Sunday that the party should “leave the issue alone.” McCain says he’s “proud” of his anti-abortion-rights stance, “but if someone disagrees with me, I respect your views.” This from a party that has longed vowed to back a constitutional amendment to ban abortion.

Here’s one GOP senator after another—Lindsey Graham, Bob Corker, Saxby Chambliss—saying he no longer feels bound by the Grover Norquist pledge against voting for tax increases. As Chambliss put it, “I care too much about my country—I care a lot more about it than I do about Grover Norquist.”

Such talk practically amounts to a revolt by a crowd that has always genuflected toward Norquist and treated his pledge like a blood oath. Refusing to raise taxes, especially on the wealthy, is close to a religious belief for the Republican faithful, and most got elected by waving the Pledge. (Their real fear was less philosophical than practical, a concern that Norquist’s Americans for Tax Reform would help foment right-wing primary challenges against them.)

And then there’s immigration reform. McCain and others in the party who watched their eventual nominee, Mitt Romney, call for “self-deportation” are now saying it’s time to find a path to legalization for millions of undocumented immigrants. Such conservative pundits as Sean Hannity agree, with Charles Krauthammer even using the word “amnesty.”

So is this a repositioning, a rebranding, or a revolution?

“Nothing focuses the attention quite like losing,” says GOP pollster Whit Ayres. “I’m pleased to see there’s some serious rethinking going on about the message and the Republican brand we present to the world.”

Ayres says the party’s losing streak in presidential politics “suggests that more than tactical change and tactical positioning is in order.” A fresh message “would seem to be a no-brainer,” he says, because if the old one was working, “we’d be looking forward to the inauguration of a Republican president.”

Few are seriously arguing that all the party needs is some minor work under the hood.

“Professional politicians at this level are no different from professional athletes at the elite level—professional actors, singers, or artists,” says veteran GOP strategist and Daily Beast contributor Rich Galen. “They looked at what happened on Nov. 6 and recognized that they have to change their position: change their batting stance, take more-commercial roles, sing songs with better melodies, and paint pictures that people want to buy.

“The issue,” he says, “is whether the Democrats will see this as reaching out the hand of bipartisanship, or as political weakness that should—must—be exploited, which was the very, very bad advice President Obama got in his first year.”

On one level, this isn’t rocket science. The Republicans recognize they have lost the popular vote in five of the last six presidential elections. The country is just over a month away from sliding off the fiscal cliff. A new CNN poll says 45 percent would blame congressional Republicans if no agreement is reached, while 34 percent would blame Obama. And in the same poll, 53 percent have an unfavorable view of the GOP.

But let’s not get carried away. It’s one thing to make conciliatory noises on talk shows, another to engage in the hard work of compromise.

On taxes—under pressure from Norquist, who is hitting back at the potential pledge-breakers—the Republicans are likely to push for a smoke-and-mirrors deal that closes loopholes and maybe caps deductions but doesn’t raise tax rates.

Says Steele: “Why are we wedding ourselves to pledges that have nothing to do with governing? If you’re a senator, your responsibility is not to Grover Norquist; it’s to the people who sent your ass to D.C.”

Obama and the Democrats, for their part, can simply sit back and let the Bush tax cuts automatically expire at year’s end, giving them the upper hand in negotiations.

On immigration, the Republicans are in such a hole with Hispanic voters, only 27 percent of whom supported Romney, that they would like the issue simply to go away. But that is not so easily accomplished; even George W. Bush couldn’t push immigration reform through a Republican Congress.

On social issues such as abortion, the GOP may simply adopt a lower profile. And when was the last time you heard a Republican complain about gay marriage, after all the punditry about how Obama would alienate a large swath of voters by embracing it? That, of course, was before voters in three states voted this month to legalize such unions—a sea change from 2004, when the Bush campaign was pushing a constitutional amendment against same-sex marriage.

For the moment, Ayres says, the party is facing not just electoral reality but the fiscal kind as well.

“If we’re not going the way of Greece, we need to figure out a way to address the situation,” he says. “Had we won the presidency and controlled the Senate, we’d have a lot more leverage in the negotiations.”