Marine Sgts. Emma A. Bringas, left, and Amaya Marin Garnica take cover while maneuvering to conduct an enemy counter attack during an exercise at Range 107, Marine Corps Air Ground Combat Center Twentynine Palms, Calif., on March 2, 2015.

WASHINGTON — Ted Cruz and Marco Rubio are supporting legislation that could put the brakes on women in the military draft, adding momentum to growing opposition on Capitol Hill.

The Republican presidential candidates confirmed Thursday that they will back Sen. Mike Lee, R-Utah, and his upcoming bill barring the White House or the courts from changing the law, which requires only men to register with Selective Service in case they need to be drafted into combat.

A bipartisan bill was introduced in the House on Thursday that would completely abolish the draft.

The sudden groundswell of opposition comes after military brass and Sen. John McCain, R-Arizona, came out in favor of drafting women. The question of fairness in the all-male draft is pressing because the Pentagon decided in December to open all positions – from boot camp to special operations -- to female troops.

“We simply can’t trust this president or the courts to honor the law and protect our daughters,” Lee said in a statement released to Stars and Stripes. “We need new legislation making clear that if the United States is going to change this policy, Congress must be the one to do it.”

Staff for Sen. Cruz, of Texas, confirmed he will be a co-sponsor of the bill. Sen. Rubio, of Florida, supports keeping any decision on the future of the draft in lawmakers’ hands.

“Sen. Rubio agrees with Sen. Lee that Congress needs to determine the future of the Selective Service system and is working on legislation to codify that role and plans to support it‎,” Rubio spokesman Alex Burgos wrote in an email to Stars and Stripes.

The Supreme Court upheld the all-male draft in 1981, finding that women could be excluded because they would not be called to fill critical combat positions during a war. But since the Pentagon began full integration of women that rationale might no longer be valid.

Marine Commandant Gen. Robert Neller and Army Chief of Staff Gen. Mark Milley testified to the Senate this month that they believe the exemption should be ended.

Lee’s staff said the bill will essentially preserve the current law and has already attracted a number of co-sponsors, such as Cruz. The senator had planned to introduce his bill Thursday but that has now been pushed back until later this month.

The House bill introduced Thursday proposes eliminating the Selective Service program, which requires all men between 18 and 25 years old to register

“Now that women are eligible to serve in combat roles and Congress debates how to proceed on the issue of draft inclusion, we should consider a full repeal of the draft and the abolition of the Selective Service,” said Rep. Mike Coffman, R-Colo., the lead sponsor of the bill.

Coffman said keeping the system, which costs about $23 million each year, makes no sense since the draft ended in 1973 after the Vietnam War and has not been considered since.

“Our all-volunteer military has given us the most elite fighting force in the history of this country,” he said in a released statement.

A bipartisan group of lawmakers have signed onto the bill, including Reps. Pete DeFazio, D-Ore., Jared Polis, D-Colo., and Dana Rohrabacher, R-Calif.

DeFazio called the Selective Service a “mean-spirited and outdated system.”

The Government Accountability Office found that if the draft is used again it would be unable to draft troops within 193 days as required and its budget would balloon to hundreds of millions of dollars.

“Not only will abolishing the Selective Service save the U.S. taxpayers money, it will remove an undue burden on our nation’s young people,” DeFazio said in a statement announcing the legislation.

Rep. Duncan Hunter, R-Calif., sponsored a bill earlier this month in protest of the military’s total integration of women and the looming issue of the draft, sparking the wider debate in Congress.

On Thursday, he said the Lee bill is a sign that opposition is growing. Lawmakers who have come out in support of changing the all-male draft have misread public sentiment on the issue and that liberals and conservatives want to stop any requirement for women to register, Hunter said.

McCain, the chairman of the Armed Services Committee, said Wednesday that he supports the recommendations earlier this month from the military. Fellow committee member Rep. Kelly Ayotte, R-N.H., said this week she is also in favor of opening the draft.

“As women serve in more roles across the armed forces, I support the recommendation of the Army Chief of Staff and the Commandant of the Marine Corps that women should register for Selective Service,” McCain said in a written statement. “It is the logical conclusion of the decision to open combat positions to women.”

tritten.travis@stripes.com

Twitter: @Travis_Tritten

