Down the hall, in the Senate, other lawmakers are pushing instead to expand the draft registration now that the Pentagon has opened combat positions up to women.
Reps. Peter DeFazio, D-Ore., and Mike Coffman, R-Colo., are spearheading an effort in the House of Representatives to see the registration abolished, calling it a waste of money considering the success of the all-volunteer force.
"There is no one who wants this except 'chicken hawk' members of Congress," DeFazio said, referring to his colleagues who push for military action without having served themselves, who he accuses of being afraid to look weak on national security by supporting closing the agency.
The Selective Service costs $24 million a year, maintaining a database of 17 million potential draftees--all male--in the event the draft were to be reinstated.
Conscription was officially ended in 1973, but all young men between the ages of 18 and 25 are required to register.
Selective Service director Lawrence Romo, while calling the agency an "inexpensive insurance policy," said it's "the true backup for the true emergency."
He'll likely find agreement from lawmakers on the other side of the Capitol building, including Sen. Carl Levin, D-Mich., the chairman of the Armed Services Committee.
Levin, who said he supports the expansion of the draft registration to include women, has the support of groups such as the Service Women's Action Network, who consider a women's exemption a sign of lingering inequality in the military.
“SWAN advocates for the inclusion of women into Selective Service,” said Anu Bhagwati, executive director of SWAN and a former Marine Corps captain, to NBC News. “Lifting the ban on women officially serving in combat is about giving qualified women the opportunity to serve and making our military stronger, and that would include having women register for Selective Service."
In making his announcement to lift the prohibition on women in combat roles, outgoing Secretary of Defense Leon Panetta warned the Selective Service to prepare for the possible increase in workload, should policymakers begin to include women in the draft registration.
The deadline for military departments to provide implementation plans is May 15.