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DENVER — Rep. Mike Coffman isn’t taking no for an answer when it comes to the Enlist Act, his proposal that would allow some undocumented immigrants to obtain a green card after serving in the military.

On Friday, the same day Coffman, R-Aurora, attended a National Republican Congressional Committee fundraiser in Denver along with Speaker John Boehner and Majority Leader Eric Cantor, Cantor’s office said they would not allow a floor vote on the Enlist Act as an amendment to the National Defense Authorization Act, or NDAA.

On Tuesday, Coffman and the two other sponsors of the Enlist Act, Rep. Luis Gutierrez, D-Illinois, and Rep. Jeff Denman, R-California, joined more than a dozen undocumented young people with hopes of joining the military and call on House leaders to reconsider at a press conference outside the U.S. Capitol.

“These extraordinarily dedicated young people want the opportunity to serve our country – the one they call home – in uniform, and to advocate for better lives for their families, neighborhoods, and communities,” said a press release from Coffman’s office Monday. “These are talented, hardworking DREAMers who will strengthen our military, boost our national security, and enhance our military readiness.”

The House Rules Committee is scheduled to meet Tuesday to consider which amendments to the NDAA will receive floor votes.

Conservative groups such as Heritage Action have fought to kill the Enlist Act.

Coffman, one of the most vulnerable incumbent Republicans in the House, has softened his stance on immigration over the last year, largely in response to his district being re-drawn to include a far larger Hispanic population than it did when he was first elected in 2008.

“There’s got to be a path down the middle,” Coffman told FOX31 Denver in an interview last week. “Let’s secure our borders, enforce our laws, let’s have immigration policies that are going to grow the economy, but let’s also be compassionate and keep families together.”

It’s been nearly a year since the Senate passed a comprehensive immigration reform package that included $40 billion in additional border security funding and a 13-year path to citizenship for undocumented immigrants and the House, which wants to take a piecemeal approach, has yet to act on any elements of immigration reform.

“As long as they do it, I don’t care if they chop it up or pass it in a comprehensive way,” said Sen. Michael Bennet, D-Colorado, one of the eight senators who authored the Senate bill. “But they haven’t done anything. Meanwhile, our high tech community is suffering as a result; our agriculture community is suffering as a result.”

Coffman’s challenger, Democrat Andrew Romanoff, also pointed out that Coffman, as a member of the House Armed Services Committee, passed up an opportunity on May 8 to introduce the Enlist Act as an amendment to NDAA in committee.

“It’s hard to understand how you share a stage with people you don’t think should be in the country to begin with,” Romanoff told FOX31 Denver Tuesday after Coffman’s Washington press conference. “But in the end, if you believe in immigration reform, you’ve got to actually vote for it, and you’ve got to stand up to your party if they won’t allow it.”