WASHINGTON–At a press conference featuring undocumented high school students in military garb and in formation, top advocates for a proposal to grant amnesty to illegal alien “DREAMers” who enlist in the military warned that President Obama could move unilaterally to enact the proposal if Congress rejects it.

Obama “has the power just by the stroke of a pen to instruct the Department of Defense to allow DREAMers with DACA to serve in the military. Just like he can with deportations,” Cesar Vargas, a pro-immigration reform activist said at the Capitol Hill event Tuesday.

Vargas was joined by GOP Rep. Jeff Denham (R-CA), who has championed the proposal and is offering as an amendment to a defense authorization bill today in defiance of Majority Leader Eric Cantor and Democratic Rep. Luis Gutiérrez (D-IL), a top congressional proponent of amnesty, Rep. Joaquin Castro (D-TX), currently pushing to allow DREAMers apply to military academies and Colorado Republican Rep. Mike Coffman (R-CO), an advocate for allowing DREAMers to enlist.

Denham told reporters Tuesday afternoon that he was “surprised” Cantor said he would block the amendment Friday. He had previously said Cantor was strongly backing his efforts.

At Tuesday’s press conference touting the proposal, called the “ENLIST Act,” the California Republican made his case for the amendment to be attached to the National Defense Authorization Bill, but noted that he would continue to fight to get a vote on the amendment as a stand alone bill, something for which House Speaker John Boehner left the door open Tuesday morning.

Denham said that he believed that the Department of Defense currently has the ability to enact what the legislation proposes.

“I think the DoD has the ability to do this today and if the military takes the position that they want the best and brightest, and these men and women meet that criteria, then I think it something the Department of Defense is willing and able to do,” Denham said.

“As a matter of military readiness and national defense, if the Department of Defense changes its criteria, that is something I that would welcome,” he added, going on to express frustration that the House has not held a full debate on the matter of immigration reform.

Gutiérrez said he hopes the amendment will be allowed on the NDAA. He said that the GOP’s blocking of the bill shows it has enough votes to pass and even go beyond.

“Yesterday Sen. [Dick] Durbin had a hearing on your very proposal on the ENLIST Act and… we heard from the Department of Defense, they told us that early this summer we are going to get an answer, and that they are looking at the regulations,” he said, referring to testimony from Jessica Wright, the Acting Under Secretary for Personnel and Readiness at the Defense Department.

“One way or another these men and women are going to be able to serve in the military. I am going to tell you what I prefer. I prefer that you allow the Congress of the United States to vote and not do it through executive action. That is that I prefer,” Gutiérrez said. “That is the best way forward and that is why I support Congressmen Denham and Coffman so much in their endeavors to get a vote. But not withstanding that, if that does happen, then I think the President of the United States not only has the responsibility but has the authority under law to make the kinds of changes that would allow the men and women here with us to serve in the military of the United States.”

At the press conference, a dozen young undocumented immigrants donning camo hats and white t-shirts (reading #DREAM ARMY) practiced drills and learned how to properly salute. Several spoke about why they believed they should be able enlist in the United States military.

“There are many potential legislative and administrative opportunities to allow us to serve in the military and wear this country’s uniform. But today is bigger than ourselves it is about the Dreams of our parents. The reason we are here is because our parents made the sacrifices to bring us to this country,” Jose Batino a 25-year-old undocumented immigrant who came to the United States from Mexico as a child, said.