WASHINGTON (CBSNewYork/AP) — The House on Wednesday overwhelmingly passed $7.9 billion in Hurricane Harvey disaster relief as warring Republicans and Democrats united behind help for victims of that storm as an ever more powerful new hurricane bore down on Florida.

The 419-3 vote sent the aid package — likely the first of several — to the Senate in hopes of sending the bill to President Donald Trump before dwindling federal disaster reserves run out at the end of this week.

READ MORE: COVID Vaccine Mandate Takes Effect For Workers At New Jersey Schools, Colleges, Universities And State Agencies

The first installment in Harvey aid is to handle the immediate emergency needs and replenish Federal Emergency Management Agency reserves in advance of Hurricane Irma, which is barreling through the Caribbean toward Florida.

“Help is on the way,” said Texas GOP Rep. John Culberson, whose Houston district was slammed by the storm. “The scale of the tragedy is unimaginable. But in the midst of all this, and all the suffering, it really reflects the American character, how people from all over the country stepped up to help Houstonians recover from this.”

“This is a chance to be your brother’s keeper,” said Houston Democratic Rep. Al Green. “This is chance for the unity that we express when we’re before the cameras to manifest itself in the votes that we cast here in Congress.”

Far more money will be needed once more complete estimates are in this fall, and Harvey could end up exceeding the $110 billion government cost of Hurricane Katrina.

“My friends and neighbors’ homes were completely flattened by Hurricane Harvey’s winds. Businesses were destroyed,” said Rep. Blake Farenthold, R-Texas. “FEMA will be out of money in just two or three days if we don’t pass this.”

Politics quickly intruded as Democratic leaders insisted they would back the measure in the Senate only if it were linked to a short-term increase in the nation’s borrowing limit, not the longer-term hike that Republicans and the Trump administration want.

And some Democrats from the New York delegation reminded Texas Republicans that they opposed a larger aid bill for those harmed by Superstorm Sandy in the Northeast five years ago.

“What you did to us during Superstorm Sandy should not stand, should not be done to any other people, any place in the country,” said Rep. Eliot Engel, D-N.Y. “We’re one country, we’re Americans. We need to help those who need help.”

In the Senate, Democratic leaders say the president has agreed with them to tie the bill to a three-month extension on government funding and a three-month increase in the debt limit, CBS2’s Alice Gainer reported.

“We had a great meeting with Chuck Schumer, Nancy Pelosi and the whole Republican leadership group,” Trump announced Wednesday.

“It was a really good moment of some bipartisanship and getting things done — no one standing in their corner,” Senate Minority Leader Chuck Schumer said.

However, Senate GOP leaders want to link a long-term increase in the debt limit — until 2019 — to the Harvey aid, but that plan faces opposition from conservatives and thus will need Democratic votes.

“I think it’s a terrible idea,” said House Freedom Caucus Chairman Mark Meadows, R-N.C., who conceded that conservatives were getting outmaneuvered. “I think at this point there are bigger issues that we have to focus on.”

READ MORE: FDA, CDC May Approve COVID Vaccine Booster Shots For Millions This Week

Earlier, House Speaker Paul Ryan had objected to the idea of linking the aid package to the borrowing limit altogether.

“We’ve got another unprecedented hurricane about to hit Florida, and they want to play politics with the debt ceiling?” he said.

Congress has until September 29th to raise the limit or the United States will begin defaulting on its loans.

House Minority Leader Nancy Pelosi, D-Calif., and Senate Minority Leader Chuck Schumer of New York want to retain Democratic influence and trying to ensure the Republican-controlled Congress addresses health care and immigration as the hectic fall agenda kicks off.

“Given Republican difficulty in finding the votes for their plan, we believe this proposal offers a bipartisan path forward to ensure prompt delivery of Harvey aid as well as avoiding a default, while both sides work together to address government funding, DREAMERS, and health care,” Pelosi and Schumer wrote.

Senate Majority Leader Mitch McConnell, R-Ky., said again Wednesday that increased Harvey costs show the importance of acting swiftly to increase the government’s debt cap to make sure there’s enough borrowed cash to pay out the surge in disaster aid.

Last week, Connecticut Senator Richard Blumenthal told WCBS 880’s Sean Adams there would be no tit-for-tat delay in providing relief for Harvey.

“We’re going to do the right thing. Two wrongs don’t make a right and we’re going to come to the aid of these folks in the Gulf Coast even though the senators from that area gave us a hard time and delayed the aid to us,” Blumenthal said.

Economists said Harvey shut down everything from plastics plants to oil refineries to the Houston port — the second-busiest in the nation.

Also Wednesday, Trump was in North Dakota where he discussed his tax overhaul plans.

“It’s not only business taxes, it’s middle income families, it’s families at every level — tax cuts,” he said.

He gave no specifics, instead saying he’ll go into “great detail” in two weeks, because they are still being worked out.

The president also said the United States is the highest taxed nation in the world. However, according to the Organization for Economic Cooperation and Development, the overall U.S. tax burden is one of the lowest among the 32 developed and large emerging-market economies, Gainer reported.

MORE NEWS: Sharee Jones Charged With Arson, Hate Crime After Fire At Brooklyn Yeshiva

(© Copyright 2017 CBS Broadcasting Inc. All Rights Reserved. The Associated Press contributed to this report.)