House Republican leaders want to strip language from a defense policy bill requiring women to register for the draft, employing a maneuver to prevent members from having to cast and up-or-down vote on the politically contentious issue.

Momentum has been building in recent weeks to make women eligible for the draft following the Obama administration’s decision to open all combat roles to women in the military. Both the House and Senate Armed Services committees have endorsed the idea in their annual defense policy bills approved in recent weeks and on Tuesday Senate Majority Leader Mitch McConnell (R-Ky.) also endorsed the idea.

“Given where we are today with women in the military performing virtually all kinds of functions, I personally think it would be appropriate for them to register just like men do,” McConnell told reporters.

But House GOP leaders are concerned about the proposed change, arguing it should be more broadly debated rather than included as part of the larger defense bill.

On Tuesday, the House adopted a rule governing overall debate for the defense authorization bill that strips the language concerning the draft on a near party-line vote. That means the language won’t be part of the overall bill when it debated on the floor this week.

Democrats immediately decried the committee’s overnight move to remove the provision concerning women in the draft.

“This is a dead-of-night attempt to take an important issue off the table,” House Armed Services Committee ranking member Adam Smith (D-Wash.) said in a statement Tuesday, taking aim at Rules Committee Chairman Pete Sessions (R-Texas) for being “so concerned about a vote on women’s equality in the military” that he spearheaded the move.

Sessions is one of a handful of Republicans who filed amendments to strip out the section of the bill expanding the draft to women. Of the 60 amendments expected to receive votes Tuesday, Sessions’ proposal is the only one that is considered approved when the rule is adopted.

Sessions’s amendment would replace the language regarding women in the draft with a requirement for a study to examine the continued usefulness of the draft and how Selective Service registration would be impacted by expanding it to include women.

“One is there has not been a review of whether we need Selective Service since 1994,” House Armed Services Chairman Mac Thornberry (R-Tex.) told reporters Tuesday. “And so my strong view is that we need to ask the big questions and figure out whether we need it. If so, for what purpose? What would happen if we did away with it? If we do have it, who’s going to be involved?”