A large, influential conservative organization backed by big donors is urging Republican House members to vote against the 2015 National Defense Authorization Act (NDAA) bill next week if it includes a measure that would grant green cards to undocumented immigrants that serve in the military.

The Heritage Action, which is the advocacy arm of the right-leaning Heritage Foundation, sent out a blast memo telling the GOP to kill the NDAA if the "ENLIST Act" is attached. Championed by Republican Rep. Jeff Denham, the ENLIST Act would give young, undocumented residents a pathway to citizenship if they enlist in the U.S. military.

There is speculation the measure might be added as an amendment to the NDAA, which authorizes $496 billion in base Pentagon spending and blocks personnel benefit cuts. Sources also say the bill could be presented on the House floor for a vote next week.

"Advancing an amnesty-first agenda on the backs of our brave men and women in the military is deplorable. The ENLIST Act creates radical and perverse incentives that will have a negative impact on our military and our immigration system," Heritage Action chief executive officer Michael Needham said in the memo, according to the Military Times.

"It has no place in a debate over the future of our military, which is currently reducing personnel," Needham said. "The House Rules Committee should keep this contentious issue out of the NDAA."

On Friday, a spokesman for House Majority Leader Eric Cantor announced that he plans to block a vote on legislation giving a path to citizenship to undocumented residents in the military, The Associated Press reported.

In addition, the Madison Project group, which supports conservative candidates and causes on Capitol Hill, released a statement condemning the ENLIST Act, according to Roll Call.

"We must make it clear to Members of Congress that, if amnesty is slipped into the NDAA, especially at a time when [President Barack] Obama is nullifying the rule of law, they must oppose the procedural rule to consider the bill," Daniel Horowitz, the Madison Project's policy director, wrote in a blog post on Wednesday. "That is the only way to defeat this travesty."