It remains to be seen whether any members of their respective caucuses, particularly hardline Republicans angry that the bill does not include deeper spending cuts, will resort to arcane Senate rules to try to stop it from passing.
The Treasury Department has warned that it will not be able to pay all of its bills on June 5 if Congress does not act.
The Republican-controlled House of Representatives approved the bill Wednesday night in a vote of 314 to 117 votes. McCarthy lost the support of dozens of his fellow Republicans.
The Senate will remain in session until a bipartisan bill is approved, Senate Majority Leader Chuck Schumer said Thursday.
“Once this bill reaches the Senate, I will move to get it to the floor as soon as possible,” Schumer said Wednesday.
His peer, Senate Republican leader Mitch McConnell, also signaled that he would work for its speedy passage, saying: “I will be proud to support it without delay.”
Democrats control the Senate by a narrow margin of 51-49 votes. House rules require 60 votes to pass most legislation, meaning at least nine Republican votes are needed to pass most bills, including the debt ceiling deal.