The GOP bill also seeks to force the Senate into passing a budget for the first time in nearly four years. Under the bill, members of Congress would have their pay withheld if their respective chamber fails to pass a budget.
Democrats did not announce when a final vote might take place, but are hoping it can be by the end of the week.
Also Wednesday, Sen. John Kerry (D-Mass.) plans to deliver his farewell speech at 2:30 p.m. on the Senate floor. The Senate confirmed him as the next secretary of State on Tuesday.