“We were all ultra right-wingers, but we figured out right quick that when you are in the majority, you have to govern,” he said of the 1994 class of House Republicans. “If you are going to govern in this country you are not going to govern on the far right or the far left. You’ve got to figure out a way to somehow get pretty close to the middle, otherwise you are going to do what we did — that is shut the government down. And we paid a heavy price for it. And you saw that again just a year ago.

“We need to find the best solution that is not a political solution and that requires hard and tough votes to be made,” Mr. Chambliss said. “And nobody around here has been willing to make hard and tough votes the last four years.”

There are fewer departing lawmakers than in the two previous Congresses, but many of those leaving are seasoned legislators. Among those exiting are Representative John D. Dingell, the Michigan Democrat and longest-serving House member in history, and Senator Carl Levin, Democrat of Michigan and chairman of the Armed Services Committee, who spent 36 years in the Senate before casting his final vote on Dec. 16.

Image Representative Henry A. Waxman of California Credit... Gary Cameron/Reuters

“Many foresee a continuation of polarization and partisanship in the Senate and say it is naïve to suggest that the next Congress might come together, break out of gridlock, and accomplish great things,” Mr. Levin said in his farewell speech. “But I know the Senate can do better because I have seen it happen with my own eyes.”

If lawmakers are to break out of the partisan cycle, Mr. Kingston said, they need to avoid being inundated by their constituents in an increasingly digital world where members of Congress find themselves under immediate pressure as events unfold.

“If new members allow their base to control their behavior up here they are going to be miserable,” said Mr. Kingston, who has seen the rising influence of Tea Party activists on Republican lawmakers. “While the voters might be yelling and screaming at you to do something, that’s not your job.