WHEN IT comes to overhauling the nation’s broken immigration system, the brawl over the government shutdown and the debt limit has left Congress in a state of suspended animation, or sustained denial. The issue will not disappear. House Republicans, the major stumbling block to reform, got a reminder of that last month when the Pew Research Center reported that the number of illegal immigrants may be rising after three years of apparent stability.

The new estimates from Pew, which said about 11.7 million undocumented immigrants are living in the United States, coincided with disheartening news that a bipartisan group of House lawmakers has disbanded after trying for four years to find a compromise on immigration. Three of four Republican members of the so-called Gang of Seven quit, including two in recent days.

Many House Republicans quake at the prospect of primary challenges and the supposed hostility of the party’s base to anything that can plausibly be maligned as amnesty for unauthorized immigrants. Their fears are not conjured from thin air: Sen. Marco Rubio of Florida, once the Republican “It Boy,” has been vilified by some conservatives since he took a leading role on the immigration bill that emerged from the Senate in June.

The lesson is hardly surprising: It takes political courage to get important things done in Washington. Few House Republican leaders have shown anything approaching Mr. Rubio’s guts on immigration.

We have chided Rep. Bob Goodlatte (R-Va.), the chair of the House Judiciary Committee, for suggesting that failing to enact an immigration bill was an acceptable course of action. More recently Mr. Goodlatte, whose committee handles most immigration bills, said he supports granting unauthorized immigrants some sort of legalized status that would permit them to stay and work in this country, though it would lack a special or certain path to citizenship.

Mr. Goodlatte floated that idea before, but he has yet to offer it as legislation. Doing so would take a dose of Rubionian courage and the resolve to confront elements in his own party that would regard legal status as a form of amnesty nearly as pernicious as the promise of citizenship itself.

By the same token, conferring legal status on millions of illegal immigrants would throw down a gauntlet to Democrats, many of whom regard it, with revulsion, as creating a new underclass of non-citizens who would be free to work but not free to vote. By introducing such a bill, Mr. Goodlatte might put Democrats in no less an awkward spot than his fellow Republicans.

At the least, it could restore momentum to a debate that has grown moribund since the Senate’s immigration bill met a brick wall with the House GOP. Until now, Republican leaders, including Mr. Goodlatte, have countenanced only stale ideas such as legislation that would turn the Southwest border into an armed camp of patrol officers and military equipment but do nothing to address the key issue of 11.7 million immigrants living here illegally. That won’t solve the problem, for the Republican Party or the country.