She had traded in her new normal in Puerto Rico — no electricity, no internet, no classes — for the suburbs of Long Island and the comforts of a Residence Inn. Aurelys Alers-Ortiz traveled with several other University of Puerto Rico law students who took up Touro Law Center’s offer to flee the devastation of Hurricane Maria and finish their semester here.

But as she returned to the rhythms of campus life, with lectures on intellectual property and copyrights and socializing with other students, her mind has often been pulled back home, where her family has stayed and where routines and livelihoods remain unraveled by the storm.

“I’m just lying in bed, with the air-conditioning,” she said, “and thinking of my mom.”

An influx of Puerto Ricans arriving in the continental United States has swelled in recent weeks, now reaching the tens of thousands, as a sluggish recovery compounds the island’s devastation. Officials in several states are grappling with how to accommodate the needs of the newcomers, who require housing and health care and are enrolling their children in school in growing numbers. In Florida, which has seen the biggest infusion of Puerto Ricans, the resettlement stands to reshape the state’s demographics and perhaps its politics.

But the population shift poses a potentially much larger challenge for Puerto Rico, as it tries to stagger back not just from the disastrous toll of Hurricane Maria but years of steep economic decline that had left the island beleaguered even before the storm’s landfall on Sept. 20. Many who are leaving are professionals, students and other young people who would be essential to recovery and setting Puerto Rico on a better course.

That has made the decision to leave a fraught one. It has stirred questions about their bonds with the island and what responsibility they bear to help it heal. It has also spurred resentment among the people left behind with some viewing the departures with envy or even as a betrayal. Many who have left believe their choice was the right one, maybe the only one, yet it has still intensified the trauma created by the storm.

“We have a degree of guilt. Everyone has a degree of guilt,” said José Camacho-Vazquez, 26, one of the students who has come to the Touro Law Center. He choked up as he described the strain of deciding to leave even for a few months — his mother encouraged him, but his father urged against it, not wanting him to leave his mother.

The resentment is “real,” he said. “But you have to do what you have to do.”

The motivation to leave is driven in large part by the dire circumstances on the island. Basic essentials are hard to find and electricity and other utilities are unreliable or entirely inaccessible. Much of the population has been unable to return to jobs or to school and access to health carehas been severely limited.

Some hope to return once the situation improves, but many have decided to build new lives wherever they have landed. “There’s no possible way I’m going back to that, to have all those problems and not have all those necessities,” said Bryan Troche, who has a marketing business and who has been staying with relatives near Orlando, Fla., along with his wife and infant daughter. “There’s no back to reality. This is the new normal.”

Francois Franceschini was able to claim a spot on one of the first ships to leave the island after the hurricane, a Royal Caribbean cruise ship being used for humanitarian runs. He described the “survivor’s guilt” he felt as he ate steak and mashed potatoes in an air-conditioned state room.

Mr. Franceschini thought he would join his family in New York City for only a few weeks, gathering generators and supplies, and then head back. But those plans quickly changed: Now, he and his girlfriend, who have been staying in his aunt’s apartment in the Bronx, are starting to look at colleges. Puerto Rico, he said, has been “taken back to the Dark Ages.”

“It got genuinely scary when it became less about comfort and more about safety and health,” he said. “I can work with not being comfortable for a while. I can’t deal with not being safe. It hurt a lot, even though my parents had already come to New York. I love Puerto Rico too much.”

Those leaving after the hurricane join an exodus that began well before the storm. In recent years, the Puerto Rican population on the mainland (5.4 million people) has grown far larger than the one on the island itself (3.3 million). The territory’s economy had been crippled by a decade-long recession and a debt crisis that pushed the island to declare a form of bankruptcy this year and forced many, faced with dwindling work prospects and a decreasing quality of life, to head north.

“The minute we got into the law school, we knew there was a very minimal amount of jobs we could acquire as lawyers working in a firm there already,” said Lourdes Carreras-Ortiz, a University of Puerto Rico law student.

But before the storm, Ms. Alers-Ortiz said, many Puerto Ricans were able to maintain at least the facade of a middle-class life: They had cellphones, went to the movies, shopped for clothes at Plaza Las Américas, a sprawling mall in San Juan. The storm washed that away. “Our first-world mask has been ripped off,” she said. “Now, we’re third world.”

“The feeling is life stopped,” she added.

Members of the diaspora, even recent arrivals, argue that they can contribute to Puerto Rico’s recovery from afar. They point to a surge of money and supplies, and they said they can push elected officials to direct more aid to the island.

A report published by the Center for Puerto Rican Studies at Hunter College projected that upward of 200,000 people could leave the island in the year after the hurricane, and that by 2019, that figure could approach a half-million people, or about 14 percent of the island’s population. Researchers anticipate the demographic shifts created by migration will spread beyond Florida and the New York metropolitan area, places that already have longstanding ties to the island, to communities across the country.

Aja Nelson had been displaced twice: She fled St. Thomas, one of the United States Virgin Islands, for Puerto Rico after Hurricane Irma, only to be pushed out again by Maria. Now, Ms. Nelson is staying with relatives in Atlanta.

“I am just shellshocked,” she said.

Jose Manuel Ureña, 24, had been a cook for the last two years at a restaurant in Condado, an upscale area of San Juan that had been popular with tourists, and also helped his brother take care of their mother. He said he had lost his job and a friend promised to help him find work in a kitchen in Newark, where he was heading.

“My plan is to get to New Jersey and work until I can’t anymore,” he said. “I can’t wait to have a home again.”

Many who left Puerto Rico described an existence that had been stripped down to its basics, their days spent collecting food, water and fuel. When Mr. Franceschini arrived in New York, he began to notice the trivial things he had once taken for granted, like when he had a cool drink. “You’re really excited over ice,” he said.

Touro Law Center is one of many schools across the country that have welcomed displaced students. A small group had come just for the semester and expected to return to their school next year, but now they realize their time away is likely not enough to restore living conditions to what they were before the storm.

“The Puerto Rican way of life is gone as we know it,” Mr. Camacho-Vazquez said. “This is a fact.”

The grim situation on the island has forced the students, who are mostly in their third year of law school, to reassess their plans after they graduate and whatever obligation they have to Puerto Rico.

“I don’t owe the government anything, but I do owe my island something,” Ms. Carreras-Ortiz said as she sat with her classmates on campus one recent afternoon. “I lived there. I grew up there. The place — not only physically the island but the people, the life there — it gave me so much, and I’m the person I am because I lived on the island.”

“I do want to go back for Puerto Rico,” she added. “If everybody who can do something just leaves, the island is gone. There’s no progress.”

“That’s the thing,” another student, Cesar Rivera, interjected. “That is very admirable, but those who leave, I cannot blame.”