Senators rejected a measure on Wednesday evening to begin debate on the bill, which required 60 votes to pass.
The legislation is backed by Senate Majority Chuck Schumer and the White House, who have urged Republican lawmakers to hastily pass aid for Ukraine before funding runs out.
However, Senate Minority Leader Mitch McConnell and House Speaker Mike Johnson have called on Democrats to include border security measures in the bill in order to receive Republican support.
Biden previously requested $106 billion in supplemental funding for the US efforts in the Ukraine and Israel, as well as the Asia-Pacific. However, the initiative has largely proven a hurdle as lawmakers have refused to throw their backing behind the legislation.
The push for funding by the Biden White House comes as the US government has repeatedly emphasized that the funds previously designated for Ukraine are nearing depletion amid ever-growing fatigue within the government over continued aid packages.