Mr. Cooper and Mr. LaTourette recounted their extreme disappointment when they joined forces to bring a budget bill based on the recommendations of the deficit commission known as Bowles-Simpson to the House floor.

That day, both men said, they had at least 100 members from both parties with them; by the time of the evening vote, that number had been whittled to a mere 38. “Tons of people said really great things about it,” Mr. Cooper said, “but when the interest groups kicked in, they dramatically changed. One member told me his favorite lobbyist would be fired if he voted for it.”

President Obama’s decision early in his presidency to allow the Democratic-controlled Congress to craft legislation like the health care law while he remained at arm’s length did not help, members on both sides said. Neither did his lack of engagement with Republicans when they were in the minority, they said.

“Obama’s biggest failing has been not reaching out to Congress,” said former Representative Mike Castle, a moderate Republican from Delaware who lost a Senate bid two years ago. “I remember being at a White House meeting with Rahm Emanuel with other moderate Republicans,” he said, referring to the former White House chief of staff, “and the president came out and spoke to us for about 30 minutes. It was a good conversation, mostly about Medicare. I don’t know if anyone in that group ever heard from him again.”

Despite the increasing polarization, the “fiscal cliff” facing Congress at the end of the year, when a series of tax increases and steep budget cuts are set to automatically begin, may force some departing members to move more to the middle, simply because the implications are too grave.

The outcome of the presidential election will almost certainly have an impact on the political interplay of the next Congress. Should Mr. Obama prevail, said members and officials from leadership offices of both parties, many Democrats may feel more compelled to attack the problems with social programs. Also, many senior Republicans, once considered among the most conservative, may feel empowered to make deals to stave off large cuts to the military.

But then again, many, like Senator Mitch McConnell of Kentucky, the Republican leader, are facing re-election in 2014, and already feel heat from the right. Mr. McConnell, who once backed Senator Rand Paul’s primary challenger in his home state, recently hired one of Mr. Paul’s aides to run his campaign.