The kick-the-fight-down-the-road solution would fund the government through Jan. 15, raise the nation's borrowing limit through Feb. 7 and require income verification for those seeking health-care coverage through Obamacare.
Utah's senior senator, Orrin Hatch, said he would back the compromise while his Beehive State colleague, Mike Lee, is expected to oppose it.
Lee and Sen. Ted Cruz, R-Tex., vowed to oppose any budget compromise that funds Obamacare, which this latest deal does. Many blame their hard-line tactics for the shutdown. A large number of Republicans have criticized them for it.
"When Republicans control only one-half of one-third of the federal government, we have to understand what is achievable and what is not," Hatch said in his strongest rebuke yet of the Cruz-Lee plan. "Too many were led to believe we could accomplish something that was never possible namely defunding Obamacare through a government shutdown."
Sen. John McCain, R-Ariz., called the shutdown "one of the most shameful" chapters in his 26-year Senate career. Sen. Kelly Ayotte, R-N.H., said she agreed with ending funding for Obamacare but disliked the Cruz-Lee plan.
"Shutting down the government was a stupid strategy," she said on the Senate floor. "I hope we never do this again."
White House Press Secretary Jay Carney said President Barack Obama applauded the deal worked out between Senate Majority Leader Harry Reid, D-Nev., and Senate Minority Leader Mitch McConnell, R-Ky. He said Obama would sign the legislation when passed.
Though Carney said there were no winners in the shutdown fight and that the economy had been harmed by it Republicans essentially capitulated to most of the Democrats' demands and the Affordable Care Act escaped nearly untouched.
The GOP's lone victory in the deal was a concession that people receiving subsidies to buy health insurance would have to prove their eligibility.
"If they put on the verification of income on Obamacare, that's a win," said Rep. Rob Bishop, R-Utah. "I mean, this is not the same thing as delaying the damn thing, but it's a win."