Several efforts have been under way in recent months to convene former governors serving in the Senate into a group that can help move legislation. Sen. Angus King, I-Maine, has hosted informal dinners, and Sens. Mike Johanns, R-Neb., and Jeanne Shaheen, D-N.H., are working to create regular gatherings in the fall.

The group might be called the Former Governors Caucus (Sen. Thomas Carper, D-Del., jokingly called it the "recovering governors' support group"). But those who believe in the idea have another name for it: the Get Stuff Done Caucus.

"The reality here is arithmetic," King said. "Nothing happens without bipartisan support, period. If that's the case, then the governors—who are a bipartisan group, pragmatic, used to solving problems—are, I think, a natural vehicle for trying to make something happen."

The common wisdom says that governors are often frustrated upon arrival in the Senate, moving from executive authority to the slower pace of a purposely deliberative legislative body.

But governors are also used to making compromises and, perhaps because they have experience with the tough retail politics practiced at the state level, many are wary of inaction. In this current hyper-partisan environment, where even innocuous legislation is difficult to pass, convening ex-governors could provide a vehicle for deals to be hashed out and compromises to be reached, lawmakers say.

"The idea behind establishing a Former Governors Caucus is to … leverage in a bipartisan manner our collective experience finding common ground, overcoming obstacles, and achieving results," Johanns said in a statement.

The number of senators with gubernatorial experience has generally been on the decline since 1945, according to estimates from the Senate Historian's Office. Although not a definitive list, figures from the office show that the number of former governors serving as senators was about 20 to 25 from 1945 to 1960, and then slowly dropped thereafter, with minor increases from the late 1980s to the early 1990s.

The 113th Congress has 11 former governors serving as senators, with eight of them elected since 2008: Sens. Lamar Alexander, R-Tenn.; James Risch, R-Idaho; John Hoeven, R-N.D.; Johanns; King; Joe Manchin, D-W.Va.; Carper; Tim Kaine, D-Va.; Shaheen; Mark Warner, D-Va.; and Jay Rockefeller, D-W.Va.

Carper pointed to Manchin and Hoeven as examples of former governors who are becoming "emerging stars in our Senate." He added: "They're going to be force multipliers."

Hoeven said he's tried to pull together former governors on issues such as Medicare reform, and notes that many of those in this current class served as governors at the same time. "To get anything done in the Senate, it's got to be bipartisan, you got to get to 60 votes. Governors do have a background of having to work on a bipartisan basis," he said. "I think that shared experience tends to draw us together."

As Manchin put it, "If the rest of the members look around at the former governors that we do have, you'll find out most of us have more of a collegiate atmosphere. We know each other, we are friends, and we make a point to be friends to have a working understanding of each other's concerns. That goes a long way."

Manchin, Alexander, King, and Carper were all involved in hashing out a compromise deal to turn back an increase in student-loan interest rates. Their plan formed the framework of the bill that eventually passed the Senate, 81-18.

When asked about negotiating with Manchin on student loans, Alexander said, "Governors are accustomed to getting results, so that makes him easy for me to work with because I was a governor, so I welcome that. It's not so much that he's a Democrat or Republican, I think it's just the fact that he's spent time, as several of us have, in leading a state and trying to get results. And, in the end, we have to get more results around here."

The lawmakers don't profess that the caucus can solve all of the Senate's problems. They still have partisan divides on certain issues, with six Democrats, four Republicans, and one independent.

King said convening such a group "doesn't guarantee results."

"But I do think it's worth trying," he said. "We've got to try whatever we can around here to develop some bipartisan approaches. Otherwise, we're dead in the water."