Caught in a time warp, destined to act out their own version of Groundhog Day, Republican strategists have reliably trotted out one of their most fearsome epithets from the 1980s and ’90s to bludgeon President Obama: liberal. In response to the president’s inaugural address, Karl Rove has made the word “liberal” the refrain of a new anti-Obama ad.

In fairness, Rove isn’t the only person caught in the rhetorical equivalent of a mullet haircut. Commentators routinely described the president’s inaugural address — in which he not only affirmed the role of an activist government, but also urged progress on gay rights, immigration and global warming — as the most liberal speech of his presidency.

That may be. But the commentary — and Rove’s broadside — managed to miss a more important point: The American public largely agrees with Obama. If he is “liberal,” so is the country.

And nowhere is that more true than on comprehensive immigration reform. While resolving the immigration issue has remained elusive for more than a decade, a solid majority of Americans now favor giving undocumented workers a way to come out of the shadows.

According to a new Associated Press-GfK poll, 62 percent of Americans favor providing a path to legal status for the estimated 11 million illegal immigrants living in the United States. That reflects a steady increase in support for comprehensive immigration reform, up from 47 percent in 2009 and 50 percent in 2010, according to the same polling organization.

The shift toward overwhelming support is largely due to a change in the hearts and minds of Republican voters, according to an AP analysis. A majority of Republicans, 53 percent, now support the idea of allowing illegal immigrants to gain legal papers, up from 31 percent in 2010.

That stunning shift speaks volumes about the power of defeat. If Obama’s first election didn’t make the nation’s changing demographics immediately apparent to the average conservative voter, his re-election — which he won partly by securing the support of 71 percent of Latinos — did.

That new tolerance is also a testament to the power of leadership, which a few thoughtful Republicans are beginning to exert on the subject of immigration. Leaders such as Jeb Bush, former governor of Florida, have long warned the GOP about the foolishness of alienating Latinos, the nation’s fastest-growing ethnic group. More recently, up-and-comers such as Florida senator Marco Rubio, who could be a presidential contender in 2016, have also taken up the cause, trying to edge fellow partisans away from the harsh rhetoric and hardline policies they have pursued on illegal immigration.

Mitt Romney’s strategists have conceded that the unwelcoming attitudes he adopted toward illegal immigrants hurt him in the general election. Many members of the Republican base seem, finally, to understand that.

That’s not to say that they all do. Though Obama has pledged to move forward immediately with comprehensive immigration reform, he is still likely to encounter resistance. The GOP has spent a decade demonizing illegal immigrants; the hostility, the xenophobia and the fear linger among some of its partisans.

In that group, an argument with newfound popularity focuses on the perceived harm that comprehensive immigration reform would do to low-income American workers — especially black men. Those skeptics claim that high unemployment rates among blacks would only be exacerbated by the absorption of so many illegal workers.

In December, Mark Krikorian, a well-known immigration critic, wrote in National Review: “Mass immigration isn’t the only cause of the deep employment problems of less-skilled black workers. It’s not even the main cause. But it’s the easiest one to remedy.”

Actually, there isn’t much connection between immigration and high black unemployment rates, as research by economist David Card has pointed out. Further, Krikorian’s screed suggests that illegal immigrants could simply be rounded up and sent back to their native countries — a policy few would support. Instead, let’s bring them out of the shadows so their labor can contribute to the rebirth of the U.S. economy.

That’s a liberal notion that most Americans clearly support.

(Cynthia Tucker, winner of the 2007 Pulitzer Prize for commentary, is a visiting professor at the University of Georgia. She can be reached at cynthia@cynthiatucker.com.)

Photo by J Valas images/Flickr