“We have to come up with something that can pass and that president will sign,” urged Sen. Lamar AlexanderLamar AlexanderSenate committee vote on DeVos postponed Cheney calls for DeVos to be confirmed ‘promptly’ With Trump pick Tom Price, cool heads can prevail on health reform MORE (R-Tenn.) who is the Republican Conference chairman. “We all know that."

Alexander noted that time to broker a compromise and push it through both houses before the Tuesday deadline had become short.

"I hope that the spirit of today and of tomorrow, and of Sunday is that we spend less time plotting about how we can defeat each other’s proposals as quickly as possible and more time working together,” said Alexander.

Sen. Kay Bailey Hutchison (R-Texas) also veered away from a hard line being drawn by some of her more conservative colleagues, noting that a split Congress would require a degree of compromise.

"Congress is split," said Hutchison. "We have a majority of Democrats in the Senate and Republicans in the House therefore, we are not going to get everything that any one of us believes is right."

The Senate is currently in period of "morning business" awaiting the outcome of the vote on the BoehnerJohn BoehnerLast Congress far from ‘do-nothing’ Top aide: Obama worried about impeachment for Syria actions An anti-government ideologue like Mulvaney shouldn't run OMB MORE plan in the House.