The 316-90 vote would refill depleted emergency accounts as Florida braces for the impact of Hurricane Irma this weekend and Texas picks up the pieces after the devastation of Storm Harvey.
It is unclear when Mr Trump plans to sign the disaster aid package, but the White House praised Congress for delivering money to Harvey victims.
President Donald Trump met with congressional leaders on Wednesday to work out a deal to attach short-term, three-month measures in the Senate to fund the federal government at current levels and raise its borrowing limit, known as the debt ceiling.
Representative Walter Jones, a Republican from North Carolina, said Trump's inconsistency and unpredictability have made it almost impossible for GOP leaders to project unity. The agreement sets the GOP-controlled Congress up for a showdown in December, and many Republicans argue that Trump has sold them out and given Democrats the upper-hand in those negotiations.
"It was intellectually close to dishonest in that he said, 'I understand you on the debt, I understand you on this, I feel your pain, but you've got to bail out the Treasurybill, '" Brat said.
"His last words, and I quote, was, 'Vote for the debt ceiling for me, ' " said Rep. Mark Walker, R-N.C., who leads a group of conservative members.
"The very first thing he was thinking was, 'Look, we have things to do, ' " Mulvaney said on "Fox & Friends".
Congress will likely have to strike a major bipartisan fiscal deal in December to raise the debt ceiling long term and keep the government open for the remainder of fiscal 2018.
Rep. Marsha Blackburn (R-Tenn.), normally a Trump supporter, said she voted no on a hurricane relief bill because it included the three-month debt limit extension as well as a three-month continuing resolution, which is what the Democrats and Trump agreed to do.
"We need to be enacting spending reforms and cuts, and an increase in the debt limit without these cuts is simply unacceptable", he added.
Most recently, Trump went against the wishes of Speaker of the House Paul Ryan (R., Wis.), and Senate Majority Leader Mitch McConnell (R., Ky.) on the issue of raising the debt ceiling.