When news of the leaked Obama proposal emerged, Rubio immediately criticized it as "disappointing to those of us working on a serious solution."

On the Democratic side, some of the distrust noted by Bono Mack is evident. Remembering similar bipartisan talks on major issues, such as the Gang of Six that spent months working on a health care overhaul in 2009 without every reaching an agreement, they want to make sure Congress gets legislation to consider.

"I know that Senator Rubio was upset with this leak," Democratic Sen. Chuck Schumer of New York told CNN on Sunday. "I am not upset. We've talked to Senator Rubio and he is fully on board with our process. And I am very hopeful that in March we will have a bipartisan bill."

Schumer said the mechanics of politics was obvious: "If a Democrat, the president or anyone else puts out what they want on their own, it's going to be different than what you have (in) a bipartisan agreement, but the only way we're going to get something done is with a bipartisan agreement."