WASHINGTON - The U.S. House signed off on crucial disaster relief Thursday for people hit by storms and fires from Puerto Rico to California, overcoming concerns from Gov. Greg Abbott that Congress had not earmarked money specifically for the victims of Hurricane Harvey in Texas.

Lawmakers voted 353-69 to provide $36.5 billion in aid for victims of hurricanes Harvey, Irma, Maria and Nate, and for those fighting wildfires across California and other western states. The Senate is expected to act next week.

All the "no" votes - including six from Texas - were cast by Republicans, many of whom opposed what they called a "bailout" of the nation's bankrupt National Flood Insurance Program.

Congressional leaders promised more aid for Texas in the coming weeks.

Although Harvey victims were included in the new aid package, it does not include some $18.7 billion that Abbott and nearly the entire Texas congressional delegation had sought specifically for the victims of Gulf Coast storm victims. Much of that would have been targeted for the Houston area.

The vote came amid Democratic criticism of President Donald Trump, who suggested on Twitter early Thursday that the government's commitment to Puerto Rico could end.

More Information Six Texansvote 'nay' The six Texas Republicans voting against the disaster aid package in the House were: Joe Barton of Arlington Louie Gohmert of Tyler Jeb Hensarling of Dallas Kenny Marchant of Coppell John Ratcliffe of Heath Roger Williams of Austin

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"We cannot keep FEMA, the Military & the First Responders, who have been amazing (under the most difficult circumstances) in P.R. forever!" Trump tweeted.

Abbott raised concerns about the aid package Wednesday, suggesting the 36-member Texas congressional delegation was getting "rolled" on the requested Harvey aid package.

The intervention of Republican House Speaker Paul Ryan, who called the governor amid a Wednesday night scramble, soothed nerves that had been rattled on the eve of the vote.

After a late night meeting with congressional leaders, members of the Texas delegation said they understood that up to $15 billion of the overall emergency spending would be slated for Texas, which suffered the first in a string of natural disasters starting in August. That includes $11 billion for anticipated flood insurance claims, and an estimated $4 billion in aid requests from Texans to the Federal Emergency Management Agency disaster relief fund, which can be used to cover direct housing assistance, home repairs, debris removal and public assistance grants.

"Texas was hit first and hardest," said Houston Republican John Culberson, a member of the House Appropriations Committee. "They're due to be paid first."

Thursday morning, hours before the House vote, Abbott's spokesman Matt Hirsch issued a statement stepping back from the governor's criticism the night before:

"Governor Abbott was assured by House leadership that as soon as November, Texas will get the disaster assistance funding we're requesting for Army Corps of Engineer projects, Community Development Block Grants, and funding for dredging Texas ports, expanding bayous and critical flood mitigation projects, among other priorities."

Puts Congress on notice

Hirsch also put Congress and Texas lawmakers in Washington on notice: "The governor will hold House leadership to that promise on behalf of Texans whose lives were devastated by Hurricane Harvey. In the meantime, the governor and the Texas delegation will continue working together as a team to help Texans recover and rebuild."

Houston-area Republican Michael McCaul, chairman of the House Homeland Security Committee, said Thursday that the Texas delegation also received assurances from congressional leadership that another funding measure for Harvey victims would come within 30 days, not in December as initially envisioned.

McCaul said Abbott, who said Texas lawmakers in Washington needed to get a "stiff spine" the day before, supported both Thursday's vote and the plan for more funding.

"He's changed messaging quite dramatically since last night," McCaul said of Abbott.

"At the end of the day it was a good process to go through with our delegation, really flagging this to our leadership that you need to take care of Texas," McCaul said.

Backers of the bill argued that the measure was necessary to replenish FEMA's nearly depleted coffers and help the debt-ridden National Flood Insurance Program, which is helping disaster victims in Texas and across the nation.

"The governor understood that this was essential to keep the flow of funding constant," Culberson said.

The bill includes $18.67 billion for FEMA's disaster relief fund, nearly $5 billion of which could be used to subsidize direct loans to Puerto Rico.

Another $16 billion is for the National Flood Insurance Program, which is nearly $30 billion in debt.

The six Texas Republicans voting against the aid package were Joe Barton of Arlington, Louie Gohmert of Tyler, Jeb Hensarling of Dallas, Kenny Marchant of Coppell, John Ratcliffe of Heath, and Roger Williams of Austin.

Barton, who co-chairs the congressional Harvey task force, has been an outspoken critic of the troubled flood insurance program, along with Hensarling and Williams.

"The NFIP urgently needs an overhaul," Williams said. "Until the House passes legislation that reforms this fractured program, I cannot support a $16 billion bailout that further kicks this problem to the future."

Insurance program woes

The flood insurance program is expected to run out of money within weeks, meaning Texas claims would not be paid. Backers of the aid package said FEMA funding soon would be exhausted also, due to the faster-than-expected draw-downs for Hurricanes Irma in Florida and Maria in Puerto Rico and the Virgin Islands.

Floor debate on the aid package was marked by special pleas for aid from representatives of Puerto Rico and the Virgin Islands, which were hard hit by Hurricane Maria.

Some echoed criticism of the administration's recovery efforts in Puerto Rico, a U.S. territory where some political leaders have been exchanging barbs with Trump.

Houston Democrat Sheila Jackson Lee, citing Trump's tweet about ending aid to Puerto Rico, accused him of turning his back on the island, much of which is still without electricity and clean water. "Mr. President, how can you abandon the American people?" she said in a floor speech. "I am here to fight for those who have been impacted by Hurricane Harvey. ... We will fight, but I will not turn my back on Puerto Rico and the Virgin Islands."

The Texas allocations come on top of $15 billion Congress approved for Harvey relief efforts in September. State officials have said the total tab from the storm could reach $100 billion or more.

"Sadly, the damage far exceeds the money we've currently funded," said U.S. Rep. Randy Weber, a Republican whose district runs from Friendswood to Galveston.

U.S. Rep. Brian Babin of Woodville, whose Gulf Coast district was hit hard, called it a "second installment in critical relief for the people of Texas."

Other Houston-area lawmakers said they were assured Congress will target more money at the area soon.

"Within the last 24 hours, House leadership has committed to Governor Abbott and to the Texas delegation that it will bring up a third, targeted relief package in the coming weeks," said Humble Republican Ted Poe.

"I will hold my colleagues in the House to their commitment."

Mike Ward and Mihir Zaveri contributed to this report.