HOUSE REPUBLICANS, who have dug in their heels against immigration reform for months, may be running out of excuses.

Congress has cleared the decks for action on non-fiscal issues by passing a budget deal that lifts the threat of further government shutdowns for the time being. In New Jersey, the Republican governor, Chris Christie, after waffling for a few weeks, signed a bill granting in-state college tuition subsidies to undocumented students brought to the United States as children by their illegal immigrant parents.

And in a new survey by the Pew Research Center, Hispanics, by a 5-to-3 margin, said it was more important to allow unauthorized immigrants to work and live in this country without fear of deportation than to put them on a path to citizenship. That idea — granting legal status short of citizenship to illegal immigrants — has been percolating in Washington for months. The fact that it is backed by a majority of Latinos, who are the nation’s largest minority group as well as the largest chunk of illegal immigrants, provides an opening for compromise in Congress, if both sides will take it.

House Republican leaders have refused to take up the immigration overhaul passed in June by the Senate, despite the fact that it would probably pass if it were allowed a vote on the floor. The main impediment is hostility from the GOP’s rank-and-file to a pathway to citizenship, even one drawn out over 13 or more years, because many conservatives regard it as amnesty.

Republican hard-liners could still insist (and many no doubt would) that providing deportation relief to more than 11 million illegal immigrants amounts to amnesty, too, even without the hope of citizenship. They would prefer mass round-ups or, for the more politically correct, “self-deportation” — a polite way of saying that local authorities should make life so miserable for undocumented immigrants, most of whom have lived and worked in this country for years, that they will simply pack up and leave. That’s a fantasy.

More realistic House Republicans, who appear to include the leadership, realize that the nation must come to terms with illegal immigrants, who are deeply woven into the fabric of communities and the economy across America. Deportation relief without citizenship may achieve that goal.

It’s not an ideal solution, and many Democrats will bristle at it. It would create a caste of what would amount to second-class citizens, authorized to stay and work but not to vote or, perhaps, qualify for certain other privileges of full-fledged citizenship. Nonetheless, something has to move the ball on immigration in Congress, where it has been stalled for more than seven years. The status quo, which during the Obama administration has included deporting around 400,000 people annually, often breaking up families in the process, is unworkable and counterproductive; it neither fixes a broken system nor meets the economy’s demand for labor. In 2014, House Republicans will be out of excuses.