With the government shutdown finally concluded, the threat of a strike on Syria on the back burner and no serious chance that the U.S. will default on its debts for at least the next 3 1/2 months, perhaps Congress can pull itself together and get back to work on stalled legislation. It should begin by tackling comprehensive immigration reform.

After all, much of the heavy lifting on this complicated and controversial issue has been done. Earlier this year, the Senate passed a sweeping bipartisan bill that calls for allowing more high-skilled and low-skilled workers into the U.S. while also establishing a new guest-worker program that includes additional protections for farm workers. It would set out a 13-year path to citizenship for the estimated 11 million immigrants who are in the U.S. illegally, but only after they paid fines and passed a background check, and after additional border security measures were put in place. It’s not a perfect plan, but it takes the kind of broad approach needed to restructure the dysfunctional system.

The Republican-led House, however, has not signed on, opting instead for a piecemeal approach. Among the separate proposals waiting to reach the floor are an enforcement bill, known as the SAFE Act, which would for the first time designate as criminals all immigrants in the U.S. illegally and would allow states such as Arizona to enforce their own immigration laws. Another bill would create a new guest-worker program that would likely please growers but leave farm laborers unprotected from abusive employers. Two other bills would expand the use of federal databases to verify the immigration status of new employees.

The two sides are far apart, obviously. But there is some reason for hope after months of stalemate. In an effort to repair some of the political damage the GOP inflicted on itself during the shutdown, some House Republicans apparently are calling for action on immigration reform to win back moderate support. If the House approved just one of its piecemeal bills, it could move to a conference committee, where Senate and House members could begin to reconcile their differences. If it goes that route, the House should pass its border security measure, which is the best of the bills introduced so far. But it’s unclear whether Speaker John A. Boehner, R-Ohio, will allow any of the bills to move forward.

The reality is that the current immigration system isn’t working for American employers, who rely on the low-wage labor that comes in over the border, or for the millions of immigrants stuck in the underground economy. That’s why a broad coalition of religious, law enforcement and business leaders has repeatedly called for a compromise.

Immigration reform can still be achieved, if only GOP lawmakers stop stalling, stop grandstanding and get to work.