"That was key," Bonjean said, pointing out times when then-Senate Majority Leader Trent Lott would try to box in the Democratic leader Tom Daschle by recruiting centrist Democrat John Breaux to bring other Democrats on board.

"While the negotiations were breaking down on issues like the tax cut or IDEA (a disabilities law), you would try to pick off members and create a bipartisan resolution," he said.

One thing that has complicated the ability to get things done behind the scenes is the influence of social media, with an expanded press corps reporting every development, often in real time.

"The media landscape has changed in this 24-hour news cycle we live in where every moment is tweeted, every utterance is put on a blog, every meeting is known before it even happens oftentimes, and it's just much more difficult to get something done these days," Manley said.

Bonjean said "sitting in a room and having it being live-tweeted out to the press" makes leaders nervous as the deadline approaches.