“The only way you’re going to bring people together here in the House is by changing the rules or at least following the current rules that we have,” Rep. Raúl R. Labrador (R-Idaho) said Friday.

The problem with that, other Republicans say, is that those demands would make the House even more ungovernable than it already is.

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

The most frequently invoked breaches of “regular order” include the spending bills that have kept the government open for the past four years. Those bills, often written in crisis, have rarely been subject to formal committee votes and have passed on the floor with a coalition of roughly 50 centrist Republicans plus most Democrats.