Washington(CNN) President Donald Trump suggested Thursday that Puerto Rico is going to have to shoulder more responsibility for recovery efforts from Hurricane Maria, saying the federal government's emergency responders can't stay there "forever."

His comments -- in which he also blamed the beleaguered island for a financial crisis "largely of their own making" and infrastructure that was a "disaster" before the hurricane -- come as Puerto Rico still reels from a lack of electricity, public health access and a rising death toll. The remarks quickly prompted cries from Democratic lawmakers, who argue that Puerto Rico still needs a lot of help, as well as the mayor of San Juan, who said they were "unbecoming" and appeared to come from a "hater in chief."

Meanwhile, Texas and Florida -- two states Trump won during last year's presidential election -- also were struck by severe hurricanes recently, but the President has made no public indication that the federal government is pulling back on its response there.

The President wrote in two separate tweets, "'Puerto Rico survived the Hurricanes, now a financial crisis looms largely of their own making.' says Sharyl Attkisson. A total lack of........accountability say the Governor. Electric and all infrastructure was disaster before hurricanes. Congress to decide how much to spend..."

He continued in a third tweet: "We cannot keep FEMA, the Military & the First Responders, who have been amazing (under the most difficult circumstances) in P.R. forever!"

Attkisson is a journalist who works for conservative Sinclair Broadcasting.

White House chief of staff John Kelly said at the White House briefing Thursday that Trump's tweet was "exactly accurate" because first responders "are not going to be there forever."

"The minute you go anywhere as a first responder, and this would apply certainly to the military, you will try really hard to work yourself out of a job," he said. "There will be a period in which we hope sooner rather than later, the US military and (the Federal Emergency Management Agency), generally speaking, can withdraw because then the government and people of Puerto Rico are recovering sufficiently to start the process of rebuilding."

A FEMA official told CNN the agency has "no hard deadline" on when it plans to pull resources from the island.

"It all will be determined by the conditions on the ground," the official said.

The official said once things are "stabilized" in Puerto Rico, FEMA will "pull back resources as appropriate," adding that's the "natural progression of a response to a disaster."

FEMA's focus, the official said, is to "move from the response phase to recovery," adding the recovery phase often takes years.

Dire situation

Trump's tweets come three weeks after the hurricane first struck the island, which remains largely without power. The death toll from the storm has risen to 45, authorities have said, and at least 113 people remain unaccounted for, according to Karixia Ortiz, a spokeswoman for Puerto Rico's Department of Public Safety.

Paul Ryan leading bipartisan delegation to Puerto Rico on Friday

The recovery has moved slowly since Maria struck the US territory on September 20, leaving most of the island without basic services such as power and running water, according to residents, relief workers and local elected officials. Hospitals throughout the cash-strapped island of 3.4 million people have been running low on medicine and fuel, and residents and local elected officials have said they expect the death toll to rise.

The water situation is so dire, the Environmental Protection Agency said in a news release Wednesday, that residents on the island have reportedly been trying to obtain water from Superfund sites -- which are bodies of water contaminated by hazardous waste. The EPA advised against "tampering with sealed and locked wells or drinking from these wells, as it may be dangerous to people's health."

Administration officials sought to downplay Trump's comments Thursday morning.

Housing and Urban Development Secretary Ben Carson, testifying before the House financial services committee, said that he has "no intention" of abandoning recovery efforts in Puerto Rico.

"They're a very important part of who we are," he said, later adding: "(Puerto Rico) should not be abandoned."

And White House press secretary Sarah Sanders reaffirmed federal support to the island.

"Our job in any disaster affected location is to help the community respond and recover from that disaster. We continue to do so with the full force of the US government and its resources in Texas, Florida, Puerto Rico and the US Virgin Islands and other affected areas," she said. "Successful recoveries do not last forever; they should be as swift as possible to help people resume their normal lives."

Democrats, however, pounced on Trump's tweets.

"Puerto Ricans are Americans, and we don't abandon each other. The federal government should stay in Puerto Rico as long as necessary," Sen. Dianne Feinstein, D-California, tweeted.

Massachusetts Democratic Sen. Elizabeth Warren tweeted, "Puerto Rico is still facing a humanitarian crisis. @realDonaldTrump seems more worried about blaming hurricane victims than helping them."

And San Juan Mayor Carmen Yulin Cruz, who has feuded publicly with the President over the federal response, said on Twitter that Trump was incapable of fulfilling the moral imperative to help the people of PR. Shame on you.!"

Puerto Rico Gov. Ricardo Rosselló said in a news conference Thursday that he called the White House looking for clarification on Trump's tweets.

"The law establishes that the aid we are getting from FEMA has to be established for the duration of emergency efforts," he said. 'It's not a decision as is, it's a law that all the resources must be available for Puerto Rico."

However Rep. Scott Perry, R-Pennsylvania, who is a member of the House foreign affairs committee, told CNN's Chris Cuomo Thursday there's only "so much" the US can do to help Puerto Rico.

"I would then again say, 'What is enough?' What is the right amount to satisfy whoever says we're not doing enough," he said on "New Day." "It's regrettable and it's sad for those people but there only is physically, humanly possible so much that any nation could do in the wake of devastation."

He continued: "I lived through it myself, a victim of floods on numerous occasions, had to clean it up, and I will tell you, nobody came to help us, we handled it ourselves."

House to vote on disaster relief

Acting Department of Homeland Security Elaine Duke will make her second trip to the island on Thursday.

House Speaker Paul Ryan will lead a bipartisan delegation visiting Puerto Rico on Friday, according to the speaker's office.

Ryan will travel to the island with House Appropriations Chairman Rodney Frelinghuysen of New Jersey and Rep. Nita Lowey of New York, the top Democrat on the panel. Puerto Rico's sole representative in Congress, Jenniffer Gonzalez-Colon, and House GOP Conference Chairwoman Rep. Cathy McMorris Rodgers also will be part of the congressional delegation.

The House of Representatives approved a $36.5 billion disaster aid package Thursday to help victims struggling to recover from a string of devastating hurricanes and wildfires. The measure now heads to the Senate, which returns from a weeklong recess next week.