A bipartisan deal to roll back sharp spending cuts known as the sequester easily cleared a procedural hurdle in the U.S. Senate on Tuesday, ensuring that the agreement will be passed and sent to President Obama in the coming days.

Senators voted 67 to 33 to end debate and proceed to final passage on the budget agreement. A final vote could come as soon as Tuesday evening if Senate Republicans agree to speed things up. Otherwise, the chamber is likely to send the measure to the White House late Wednesday.

Passage of the budget measure was secured Monday when Sens. Orrin G. Hatch (Utah) and Johnny Isakson (Ga.) joined fellow Republican Sens. John McCain (Ariz.), Susan Collins (Maine) and Ronald H. Johnson (Wis.) in announcing they would help the Senate’s 55 Democrats assemble the 60 votes needed to clear a critical procedural vote and end debate on the budget measure.