With the abrupt withdrawal of Rep. Kevin McCarthy from the race to succeed outgoing House speaker John Boehner, the apparent lack of a alternative candidate with broad support who is eager to run, and deep divisions between moderates and hard-line conservatives, the Congressional Republican caucus appears to be in disarray.

The conservative, Tea Party-influenced section of the caucus, however, is seeking changes to the rules under which the House operates in exchange for falling its support for a potential new leader. Other Republicans fear, however, that such changes would make the House even more ungovernable than it already is.

The changes conservative Republicans want to see would give House committees more authority, and rank-and-file members a greater role in setting the legislative agenda for the chamber.

“Anything we do has to make it possible for the leadership to be able to lead the group and I think that’s the most important thing -- it’s about members’ initiatives, it’s about getting members’ legislation on the floor, even if it’s voted down,” Rep. Rep. James B. Renacci of Ohio told Roll Call.

Rep. Jim Renacci, of Ohio, has proposed that if a lawmaker can get 150 or 200 signatories on a bill, that bill should be guaranteed a hearing in a relevant committee and presumably a vote on passage. The goal of such rules changes, he told USA Today, is that "members are empowered in some ways to bring legislation forward to have a vote on it and have their voices heard."

Renacci's views have been echoed by a number of other conservative House Republicans, who are frustrated that they are unable to get bills on issues that are important to them onto the house floor. The bloc is calling for the implementation of so-called “regular order,” under which bills rise from committees, to the House floor, to the President for approval.

A questionnaire for speaker candidates drawn up by the Freedom Caucus, a Congressional alliance of conservative Republicans, which was first published last week by Politico, outlined the group's demands. These include greater representation for rank-and-file members on the influential Republican Steering Committee; adherence to the “Hastert rule” which requires a majority of Republicans to support any bill brought to a floor vote; and an end to retaliation for opposing leadership on procedural votes.

“Everyone tries regular order, and nobody succeeds at it,” John Feehery, who served as an aide to former speaker J. Dennis Hastert of Illinois told the Washington Post. “What will end up happening is that conservatives will lose, because they don’t have the votes.”

Following McCarthy's withdrawal, conservative Republicans are rallying around Rep. Daniel Webster of Florida, while others in the party are pushing former vice-presidential candidate Paul Ryan to run.