House Armed Services Committee Chairman Rep. Mac Thornberry (R-Tex.) will attempt to replace language on women in the draft with an amendment to the annual defense policy bill. (Octav Ganea, Mediafax/AP)

The chairman of the House Armed Services Committee this week will try to strip language from legislation he oversees that would require women to register for the draft, blaming himself for not stopping the proposal from getting in the bill in the first place.

Rep. Mac Thornberry (R-Tex.) on Monday said he “didn’t probably do everything I should have” to keep an amendment from Rep. Duncan Hunter (R-Calif.) that would enact the policy change from being added to the annual defense policy bill when it was considered by his committee.

The success of the amendment surprised many GOP members and even Hunter voted against his own proposal. Hunter said he only offered it to start a “discussion” about the Obama administration’s recent decision to allow women to serve in any combat role, a policy change he opposes. The Pentagon has not taken a position on Hunter’s amendment but top military officials have supported the idea of including women in the draft during congressional testimony.

Thornberry voted against Hunter’s amendment too, but since the committee adopted the proposal last month the idea of including women in the draft has only picked up steam, earning the endorsement of the Senate Armed Services Committee last week as well.

Thornberry told a Washington Post editorial board meeting on Monday that when the annual defense policy bill comes to the floor this week he will offer an amendment that would strip Hunter’s language because members “haven’t had a chance to look at this.”

Hunter’s amendment seeks to replace the language requiring women to register for the draft with a proposal to commission a study examining the role and usefulness of the Selective Service.

“I still believe that we need to step back and take a broader look at whether we need it or not before ever get into who is involved,” he said.

But in order to give the full House a chance to vote on the matter, Republican leaders will have to go through a few procedural calisthenics because it could run afoul of the chamber’s rules regarding the cost of legislation.

Last week, the Congressional Budget Office (CBO) found that including women in the draft actually lowers government costs by reducing spending on Pell Grants. In order to a receive Pell Grant, a student must register for the Selective Service. CBO projected requiring women to sign up for the draft would save the government money because enough female students would not do so and would therefore be ineligible for a Pell Grant.

It’s against House rules to offer an amendment that would raise the cost of legislation. Hunter’s proposal wouldn’t cost much, $7 million in fiscal 2018 by CBO’s estimate, but it is creating a procedural headache for Thornberry.

“All of that means this is complicated to even have a debate on,” he said. “So I don’t know what’s going to happen.”

Thornberry said the only likely solution is for the Rules Committee finding a procedural workaround.

“They’re going to have to because otherwise, we can’t even have a debate on it, which is crazy,” Thornberry said.

A spokeswoman for the House Rules Committee declined on Monday to comment on Thornberry’s amendment.

Thornberry’s amendment is one of a handful that have been filed to remove or otherwise change the provision dealing with the Selective Service. An amendment from Rules Committee Chairman Pete Sessions (R-Texas) would strike Hunter’s amendment, while a measure from Rep. Reid Ribble (R-Wisc.) would dispense with the Selective Service entirely. A measure from Rep. Tulsi Gabbard (D-Hawaii) would eliminate the federal penalties for failing to register.