House Majority Leader Kevin McCarthy, the most-likely-to-win candidate to replace outgoing Speaker John Boehner, ducked reporters outside the Capitol Hill Club on Tuesday evening. McCarthy went in and came out of a back door of the event, refusing to speak with nearly 30 reporters from a variety of television and print outlets camped outside.

McCarthy was in the Capitol Hill Club, a function hall and restaurant building for Republicans right next door to the Republican National Committee (RNC) headquarters, to meet with somewhere between 40 and 50—maybe more—House conservatives as he seeks to shore up support in a contentious speakership election after Boehner’s resignation announcement a couple weeks ago.

A black SUV with tinted windows picked up the Majority Leader in an alley on the side of the building so that he could avoid speaking to the press waiting out front. Several House members from the various conservative groups came out to speak to the media, including McCarthy’s two opponents for the speakership: Rep. Daniel Webster (R-FL) and House Oversight Committee chairman Rep. Jason Chaffetz (R-UT).

McCarthy’s ducking of the media comes after a gaffe on Benghazi which jeopardized the credibility of the House Benghazi Select Committee. The gaffe, in which McCarthy suggested the Committee was created for political purposes, has haunted him as he’s moved forward with his speakership candidacy. McCarthy has canceled several media interviews as he’s worked to shore up support among Republicans and hasn’t been speaking to media much at all since then.

McCarthy was meeting with conservatives from the House Freedom Caucus, the Conservative Opportunity Society (COS), the House Liberty Caucus and the House Tea Party Caucus. Only two chairmen from those respective groups—Reps. Steve King (R-IA) and Tim Huelskamp (R-KS), of COS and the Tea Party caucus, respectively—spoke with media. Rep. Jim Jordan (R-OH), the chairman of the Freedom Caucus, and Rep. Justin Amash (R-MI)—who chairs the Liberty Caucus—also didn’t speak with the media outside.

In his press availability outside, Chaffetz promised a new direction for leadership.

“There are a lot of members who are disaffected,” Chaffetz said when asked by Breitbart News what members are looking for in a new Speaker. “I think they need to see some serious process reform. If we can get the process better, then I think you get more buy-in to the main product. This group in particular is very concerned about reform and they want to see more bills and more amendments coming to the floor.”

Webster told reporters outside that he “thought the meeting went very well” and he “presented my case.”

Webster said his pitch to the members was for a “principle-based, not power-based system.”

In a previous exclusive interview with Breitbart News, Webster further expanded on that point.

“I have one desire: That is to have a principle-based, member-driven Congress. Period. That’s what I want,” Webster told Breitbart News exclusively previously.

Really, right now, the default of every legislative body I’ve been to—and I’ve been to a lot of them—is a power-based system as opposed to principle-based. That works too, you can do it that way where a few people at the top of the pyramid make all of the decisions. We’d rather see a flattened down pyramid of power and spread out the base so every member has an opportunity to be successful.