The senators agreed to invoke cloture on a motion to proceed to the legislation in a 77-19 vote on Tuesday.
The legislation, dubbed the Continuing Appropriations Act, would fund the federal government through November 17 to give lawmakers more time to pass full spending bills. The legislation also includes more than $6 billion in military and economic assistance for Ukraine.
Some Republican lawmakers in the House of Representatives have expressed opposition to including Ukraine aid in a government funding measure, as well as passing a short-term funding bill altogether, setting up a potential showdown between the two chambers of Congress.
House Speaker Kevin McCarthy reportedly told colleagues late Tuesday that he intends to amend the measure in order to include the lower chamber's border security package.
A shutdown is expected to unfold midnight Saturday; however, it remains unclear as to whether McCarthy will be able to green light the initiative as some hardline conservatives have threatened to oust the California lawmaker from the speakership.