Sens. Evan Bayh (D-Ind.) and Lindsey Graham (R-S.C.) are together asking their respective party leaders to hold monthly bipartisan lunches.

In a joint letter to Senate Democratic Leader Harry Reid (Nev.) and Senate GOP Leader Mitch McConnell (Ky.), the two lawmakers stressed that monthly, informal lunches including all 100 senators could promote "bipartisan cooperation and principled compromise" at a time when both are "needed more than ever."

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"We believe the American people would be well served if both parties agreed to sponsor monthly meetings where all senators could gather together to informally discuss pressing issues," Bayh and Graham wrote.

"We are under no illusion that such meetings are a panacea that will lead to easy agreement," they said. "We do believe, however, that bringing all senators together on a more regular basis will maximize the chances of reasoned discourse, and that the informal exchange of ideas is fertile soil for problem solving."

Lawmakers already meet every week for individual caucus lunches, but those informal policy discussions are segregated by party.

While the two lawmakers did acknowledge those meetings serve an "important party-organizing function," Bayh and Graham stressed their proposed bipartisan monthly meetings could "maximize the chances of reasoned discourse," later adding, "the informal exchange of ideas is fertile soil for problem solving."

"These joint meetings would also send an important signal to Americans who are losing faith in the ability of both parties to solve our collective challenges," the two senators wrote. "We know the American people want us to work together and we should prove to them that we are listening."

However, Graham said he hasn’t yet received any feedback from senators on the proposed lunches.
 
“We probably should start with plastic forks and knives for the first one’s just to see how this works," he told CBS' "Face the Nation" on Sunday morning.

Jordy Yager contributed to this post.