A plan to allow some young people to serve in the U.S. military even if their parents brought them to America illegally as young children may be the opening some Republicans need to support at least limited immigration reform. The so-called ENLIST Act would grant to undocumented young immigrants the right to join the U.S. military and be eligible for citizenship after four years.

But the measure already suffered one defeat when its sponsor, Rep. Jeff Denham, R-Calif., tried to add it as an amendment this week to a must-pass defense policy bill. Still, Speaker John Boehner, R-Ohio, and House Majority Leader Eric Cantor, R-Va., both have said they don’t have a problem with the principle of allowing so-called “DREAMers” to serve in the military and earn an expedited path to citizenship.