"I don't have that same kind of confidence in the House," he said.
Rep. Mick Mulvaney, R-S.C., told CNBC that a proposal could just as easily come from the House. "I expect to be meeting all night tonight."
Mulvaney, a member of the tea party, said he remains focused on Obamacare.
"What we've asked for all along, and we've never really heard from the administration why it's unacceptable, was the one-year delay in the individual mandate" in the Affordable Care Act.
Mulvaney said there has been no formal response from Senate Democrats or the White House on the Obamacare-linked proposal.
Tester said that much of what has taken place in the past two weeks has been driven by politics rather than policy concerns. "It's probably done some pretty great things for Senator (Ted) Cruz's fundraising, but it hasn't done much for this country."
"These political stunts need to stop," he said.
—By CNBC's Matt Twomey. Follow him on Twitter