"We will keep working until the job is done," Senator Schumer said in a floor speech, adding that the Senate will begin the process of passing the legislation on Thursday.
The chamber has just four days left to pass the measure - which would suspend the limit through Jan. 1, 2025 - and send it to President Joe Biden to sign, averting a catastrophic default.
"Time is a luxury the Senate does not have," Schumer said on Thursday. "Any needless delay or any last-minute holdups would be an unnecessary and even dangerous risk... The vast majority of senators recognize that passing this bill is supremely important."
Schumer said on Wednesday that the Senate would not make any amendments on the bill, which, if done, would send it back to the House for re-approval.
His counterpart, Senate Republican Leader Mitch McConnell, also signaled on Wednesday that he would work for fast passage, saying, "I'll be proud to support it without delay."
The bill, negotiated by President Joe Biden and Republican House of Representatives Speaker Kevin McCarthy, which would suspend the debt limit, essentially temporarily removing it, in exchange for a cap on spending.
It remained to be seen whether any members of their respective caucuses, particularly hardline Republicans angry the bill did not include deeper spending cuts, would use the Senate's arcane rules to try to slow down its passage.
The measure faces opposition from the right, with some Republicans angry the spending cuts weren't deeper, and left, with some Democrats opposed to new work requirements imposed on some antipoverty programs. But most lawmakers acknowledged they could not stomach the prospect of barreling ahead into default.
Biden's Democrats control the Senate by a thin 51-49 margin. The chamber's rules require 60 votes to advance most legislation, meaning at least nine Republican votes are needed to pass most bills, including the debt ceiling deal.
The last time the United States came this close to default was in 2011. That standoff hammered financial markets, led to the first-ever downgrade of the government's credit rating and pushed up the nation's borrowing costs.`