U.S. Army Capt. Kristen Griest, left,  Maj. Lisa Jaster, center, and First Lt. Shaye Haver, right, pose together after an Army Ranger School graduation ceremony, Friday, Oct. 16, 2015, in Fort Benning, Ga.  Jaster, who is the first Army Reserve female to graduate the Army's Ranger School, joins Griest and Haver as the third female soldier to complete the school. (AP Photo/Branden Camp)
U.S. Army Capt. Kristen Griest, left, Maj. Lisa Jaster, center, and First Lt. Shaye Haver, right, pose together after an Army Ranger School graduation ceremony, Friday, Oct. 16, 2015, in Fort Benning, Ga. Jaster, who is the first Army Reserve female to graduate the Army's Ranger School, joins Griest and Haver as the third female soldier to complete the school. (AP Photo/Branden Camp) Credit: Branden Campโ€”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, a Texas Republican, on Monday said he โ€œdidnโ€™t probably do everything I should haveโ€ to keep an amendment from Rep. Duncan Hunter, a California Republican, 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 GOP leaders and Hunter, who voted against his own proposal. Hunter said he only offered it to start a โ€œdiscussionโ€ about the Obama administrationโ€™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 Hunterโ€™s amendment but top military officials have supported the idea of including women in the draft during congressional testimony.

Thornberry voted against Hunterโ€™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 ย Monday that when the annual defense policy bill comes to the floor this week he will offer an amendment that would strip Hunterโ€™s language because members โ€œhavenโ€™t had a chance to look at this.โ€

Hunterโ€™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.

โ€œI 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,โ€ 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 chamberโ€™s rules regarding the cost of legislation.

Last week, the Congressional Budget Office 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.

Itโ€™s against House rules to offer an amendment that would raise the cost of legislation. Hunterโ€™s proposal wouldnโ€™t cost much, $7 million in fiscal 2018 by CBOโ€™s estimate, but it is creating a procedural headache for Thornberry.

โ€œAll of that means this is complicated to even have a debate on,โ€ he said. โ€œSo I donโ€™t know whatโ€™s going to happen.โ€

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

โ€œTheyโ€™re going to have to because otherwise, we canโ€™t even have a debate on it, which is crazy,โ€ Thornberry said.

A spokeswoman for the House Rules Committee declined on Monday to comment on Thornberryโ€™s amendment.