Updated 7:18 p.m. | House Republicans could vote as early as this week on some changes to their official rules — including a plan to diversify the makeup of the powerful Steering Committee, Conference Chairwoman Cathy McMorris Rodgers told CQ Roll Call Tuesday.  

Fast-tracking a vote to broaden member representation of the board that makes committee assignments could have an immediate effect on Republicans Kevin Brady of Texas and Pat Tiberi of Ohio, who are vying to succeed Paul D. Ryan as chairman of Ways and Means. Ryan is poised to become the next speaker Thursday.  

“That’s under consideration right now,” said McMorris Rodgers, R-Wash. “That’s one where, I think, there’s broad agreement that this is something that should be looked at.”  

Critics have argued that party leaders and leadership favorites have too much clout in the current Steering Committee makeup, crowding out important voices from the rank and file and the conservative contingents of the conference.  

Republican Policy Committee Chairman Luke Messer, R-Ind., who with McMorris Rodgers has been hosting meetings with members to discuss an array of rules changes, told CQ Roll Call Monday night that lawmakers were not concerned about changing the makeup of the Steering Committee expressly because of the race for the Ways and Means chairmanship.  

House Republicans from across the conference’s ideological spectrum have, in fact, for weeks been discussing the need to open up membership on the Steering Committee, ever since Speaker John A. Boehner announced his intention to resign and well before Ryan emerged as Boehner’s heir apparent.  

However, Messer conceded it was “fair to say that opening up the Steering Committee could have an impact on the selection” of Ryan’s successor at the helm of the influential tax-writing panel.  

Ryan applauded the effort in a statement late Tuesday, saying Americans “have lost faith in how this place works” and that “naming a new speaker alone isn’t enough to fix it.”  

There are currently 33 Republicans on the Steering Committee. Everybody has one vote, except for the speaker, who has five, and the majority leader, who has two. The panel is composed of members of elected leadership, representatives from 11 regions, plus the “small states” and Texas, which boasts the largest GOP contingent of any of the congressional delegations.  

There are also representatives from the 112th, 113th and 114th Congresses, and the chairmen of six committees: Appropriations, Energy and Commerce, Financial Services, Rules, Budget and Ways and Means.  

Under this configuration, if Ryan is technically still Ways and Means chairman and speaker-designate at the time of an election for a new committee chairman, he could have six votes to throw behind the candidate of his choice.  

If Boehner is involved in the election process, he could use his clout to back Tiberi, a fellow Ohioan and a close ally and friend. Tiberi now sits on the Steering Committee as a regional representative, and was the lawmaker who organized the purchase of a new set of golf clubs for Boehner as a going away present from the Buckeye State delegation. Brady, who is appealing to colleagues based on his seniority over Tiberi on Ways and Means, has a case to make that this is his time: He stepped aside in advance of the 114th Congress in his bid for the chairmanship out of deference to Ryan, a GOP star who had repeatedly called wielding the Ways and Means gavel his “dream job.”  

Ultimately, Brady’s Texas ties could have an impact. On the one hand, Texans are always eager to have one of their own at the leadership table. On the other, there are already six Lone Star State Republicans with committee gavels, and there’s chatter that the delegation’s stature in the conference has gotten out of control. Texans currently lead the Agriculture, Armed Services, Financial Services, Homeland Security, Rules and Science committees.  

Texas Republicans could decide that rallying behind Brady draws attention to their outsized influence. Still, regardless of the Ways and Means race, they might embrace a chance to even have more room to maneuver on the Steering Committee.  

“I haven’t been pushing for it but I think it makes sense,” Republican Study Committee Chairman Bill Flores, R-Texas, said of changing the rules so Steering Committee representation is fairer.  “I’m part of a 57 percent of the conference that only has about 20 percent representation on the Steering Committee.”  

McMorris Rodgers and Messer sent a letter to colleagues Tuesday evening drawing out details of proposed rules changes suggested by members over the past few seeks.  

They wrote that in addition to “redefining the Steering Committee structure to better reflect the makeup of our Conference,” House Republicans have also expressed interest in “developing more formalized processes to help our Conference work through differences.”  

The letter also lists members’ expressed interest in “empowering individual Members through procedures designed to enhance every Member’s ability to have their voice heard” and facilitating a return to “regular order.”  

Though they made no mention of action this week, McMorris Rodgers and Messer told members “specific recommendations should be voted on by the entire Conference in time to be implemented by the first week of the new year.”  

But Messer, like McMorris Rodgers, told CQ Roll Call there was hope to begin the process sooner than later: “A good faith, down payment now with a promise of a fuller note in the long run.”