And if Republicans take control of the Senate, the group will probably compound the difficulties House and Senate Republican leaders will have finding legislative unity.

“Obviously I’m interested in the House going forward with the Senate, and I think there are going to be a lot of challenges,” said Representative Spencer Bachus, Republican of Alabama, who will retire in January and likely be replaced by Gary Palmer, who has helped lead the Alabama Policy Institute, a conservative think tank. “A lot of the people who have sat down to solve problems are leaving, those like me that are concerned about the dysfunctionality.”

As for their replacements, Mr. Bachus said: “I think they love their country every bit as much as we do. I think maybe they’re not as pragmatic.” Mr. Bachus is one of 26 House veterans who are retiring or running for the Senate or were defeated in the primaries.

Few people know Mr. Hall or Mr. Bachus, or the departing Representatives Howard Coble of North Carolina, Tom Petri of Wisconsin or Steve Daines of Montana, outside their districts. In the coming years, they are far more likely to know their flamboyant replacements. Even the conservative firebrand Paul Broun of Georgia, who is leaving the House, is likely to be replaced by Jody Hice, a radio host and Southern Baptist pastor who may be even more conservative.