One of the few House Republican proposals aimed at allowing some undocumented immigrants to become legal U.S. residents was blocked Friday by a powerful committee chairman, who said he would not allow the measure to move forward in his bill.

The decision by House Armed Services Chairman Howard “Buck” McKeon (R-Calif.) further lowers the odds that any immigration reform proposal will pass in the Republican-controlled House this year.

The move could also cause political trouble for a half-dozen House Republicans who represent districts with growing immigrant communities. They are expected to face well-funded campaigns by Democrats and immigration rights groups to unseat them in the fall.

Two of them, Reps. Mike Coffman (Colo.) and Jeff Denham (Calif.), have been touting proposals that would allow qualified undocumented immigrants to enlist in the U.S. military and then seek to become legal permanent residents if they met certain service requirements. Other Republicans, mostly from western states, have been pressuring GOP leaders to allow votes on the proposals or include them in the National Defense Authorization Act, a comprehensive bill that is considered must-pass legislation.

But McKeon said Friday that he will not allow either proposal to be added to the defense bill, saying it is not the appropriate legislative vehicle for them. The decision came after several days of loud objections from conservative Republicans, who first learned about the possibility of including Denham’s proposal in the defense bill from reports in conservative news outlets.

McKeon said in a statement Friday that he had heard from colleagues “on both sides of this issue. They have made sound arguments and raised valid concerns, and my colleagues and friends Congressmen Denham and Coffman deserve a great deal of credit for responsibly raising the matter. This is an important issue that I know will continue to be debated going forward.”

Aides to Coffman and Denham said Friday that they would continue seeking ways to hold votes on the proposals.

Whether immigration ever becomes a topic of debate in the House this year remains unclear. After trumpeting a list of immigration principles at their annual policy retreat in January, GOP leaders quickly retreated and cast doubt that the House could take up the issue, blaming distrust of President Obama.

On Saturday, groups across the country will participate in “Two Million Too Many,” a day of protests focused on the Obama administration’s deportation policies. In Washington, advocates said they will hold a rally and march from Lamont Park in Mount Pleasant to Lafayette Park. Two families of undocumented immigrants who were deported also plan to have a presence in front of the White House each day starting Saturday.

Obama told advocates in a meeting at the White House last month that he has asked the Homeland Security Department to undertake a review of its enforcement policies. The president has said he is legally powerless to broaden a 2012 decision deferring the deportations of undocumented immigrants brought to the country illegally as children.