Senate Majority Leader Mitch McConnell of Ky., accompanied by Sen. John Thune, R-S.D., right, meets with reporters on Capitol Hill in Washington, Tuesday, Feb. 24, 2015. (J. Scott Applewhite/AP)

CONGRESSIONAL REPUBLICANS are so busy this week flirting with a partial government shutdown — their target is the Department of Homeland Security and its 240,000 employees — that they may have missed fresh evidence of how badly out of step with the American public they are on the issue of illegal immigration.

It is precisely that issue that has driven the GOP to the brink of a funding cutoff for DHS, a move that would trigger furloughs for some 30,000 employees; force tens of thousands more to work without pay; freeze grants for law enforcement agencies nationwide; and further debilitate an already demoralized department that includes the Secret Service, Coast Guard and Customs and Border Protection.

As it happens, 60 percent of Americans — and roughly equal segments of Republicans, Democrats and independents — oppose the GOP’s tactic of threatening homeland security funding as a means to subvert the Obama administration’s immigration policy. According to a new CBS News poll, a clear majority thinks the department’s funding “should be kept separate from immigration policy.”

Yet even on immigration policy, the GOP is at sea. Hard-line Republicans in the House refused to take up a bill passed by the Senate in 2013, with moderate GOP support, that would have laid out a path to citizenship for 11 million illegal immigrants. They also refused to devise any alternative legislation to address the question of how to handle those undocumented immigrants — even to grant them legal status short of citizenship.

Instead, most House Republicans insist on somehow “securing” the border before they will discuss the fate of the undocumented, without defining what would constitute a secure border or acknowledging that by virtually every objective measure it is currently more secure, and under tighter federal surveillance, than at any point in decades.

Meanwhile, Americans are approaching a consensus on the issue, and in a very different place. In a large and important new survey, majorities in all 50 states favored a path to citizenship for illegal immigrants. More than three-quarters of Americans supported either citizenship or legal status for them. By contrast, just 19 percent wanted to identify and deport illegal immigrants.

The results of the survey, based on 50,000 interviews conducted last year by the nonpartisan Public Religion Research Institute, are striking. They suggest that Americans are far more united on the question of illegal immigration than they are on same-sex marriage or abortion. Overall, 60 percent of those surveyed supported citizenship for illegal immigrants if certain requirements were met. Even in Wyoming, the most illegal-immigrant-skeptical state surveyed, advocates for a path to citizenship outnumbered deportation backers, 52 percent to 38 percent.

Increasingly, Republicans who use illegal immigration as a wedge issue are at odds not just with the Obama administration, Democrats and Hispanics; they are also at odds with majorities of Americans in every region of the nation. That’s a recipe for political marginalization.