The U.S. economic recovery from the pandemic has been stronger and more durable than many experts had expected, and a rebound in immigration is a big reason.

A resumption in visa processing in 2021 and 2022 jump-started employment, allowing foreign-born workers to fill some holes in the labor force that persisted across industries and locations after the pandemic shutdowns. Immigrants also address a longer-term need: replenishing the work force, a key to meeting labor demands as birthrates decline and older people retire.

Net migration in the year that ended July 1, 2023, reached the highest level since 2017. The foreign-born now make up 18.6 percent of the labor force, and the nonpartisan Congressional Budget Office projects that over the next 10 years, immigration will keep the number of working Americans from sinking. Balancing job seekers and opportunities is also critical to moderating wage inflation and keeping prices in check.

International instability, economic crises, war and natural disasters have brought a new surge of arrivals who could help close the still-elevated gap between labor demand and job candidates. But that potential economic dividend must contend with the incendiary politics, logistical hurdles and administrative backlogs that the surge has created.

Visits to Texas on Thursday by President Biden and his likely election opponent, former President Donald J. Trump, highlight the political tensions. Mr. Biden is seeking to address a border situation that he recently called “chaos,” and Mr. Trump has vowed to shut the door after record numbers crossed the border under the Biden administration.

Since the start of the 2022 fiscal year, about 116,000 have arrived as refugees, a status that comes with a federally funded resettlement network and immediate work eligibility. A few hundred thousand others who have arrived from Ukraine and Afghanistan are entitled to similar benefits.

But far more — about 5.5 million — have been apprehended at the borders and at airports and seaports. Not all are allowed to stay, but a vast majority of those who do receive little government assistance. People seeking asylum have faced long delays before they can work legally, and a busing campaign by Southern governors has concentrated them in a few cities that are struggling to absorb them.

Labor needs are often greatest elsewhere. Steve Snyder, a business agent for Plumbers and Steamfitters Local 157 in Lafayette, Ind., and the president of the City Council, says his union is desperate for new members, especially given the new infrastructure work available in the region.

“I would welcome them with open arms, put them up in a hotel and try my damnedest to get them plugged into our community, because we do have the need,” Mr. Snyder said. “It’s going to be expensive, it’s going to be uncomfortable, but it’s something that, in my opinion, needs to happen.”

Immigrants have re-energized shrinking towns and cities before. Anuj Gupta runs the Welcoming Center, a nonprofit in Philadelphia that was founded 20 years ago in an effort to reverse population decline by attracting immigrants. “This should be as bipartisan an issue as an issue can get in 2024 because the economy demands it, employers want it, and the individuals who are coming, they’re in search of work,” Mr. Gupta said.

The Biden administration acted to move migrants into the work force by extending temporary protected status to Venezuelans who were in the United States before July 31, 2023, a move covering 472,000 people. It has also expanded the use of humanitarian parole for people coming from countries in turmoil, including Cuba, Haiti and Nicaragua; the designation generally lasts two years and requires that applicants have a financial sponsor in the United States.

People in those categories are immediately eligible for work permits, but they still have to be processed. The asylum process offers the prospect of legal work, but requires waiting at least six months after applying for asylum. In 2022, it took a median of nine months to process one of those permits.

State and local governments in New York and Illinois kicked into high gear toward the end of last year to get paperwork moving. Agencies began hosting mass document processing events to get people in the pipeline, and hiring fairs for those who had made it through. Median turnaround times for work permits for asylum seekers and parolees are now under a month.

As a result, the number of work authorizations given to people seeking or granted asylum, refugees, and those covered by temporary protected status and parole rose to more than 1.2 million in 2023 from about 423,000 in 2022, according to data from U.S. Citizenship and Immigration Services.

But completing the paperwork is still a significant bottleneck. The number of adults streaming over the border continues to outpace the number of work-permit applications that have been submitted. They are difficult for non-English speakers to complete without legal assistance, which is in short supply, and often require fees and a consistent mailing address.

Catholic Charities of the Archdiocese of New York has helped thousands with the paperwork process for work authorizations. It also trains immigrants for specific roles, like nannies, and offers safety training required for construction work.

One of the beneficiaries has been Edgar Alayón.

Mr. Alayón, 32, was an accountant in Venezuela before he started getting pushed out of jobs because he didn’t support the Venezuelan government. He arrived in the United States in May, and Texas was offering free flights to New York, where, he had heard, the city would provide shelter.

Mr. Alayón was granted parole, but he didn’t work before receiving his employment authorization in December. That allowed him to pick up jobs in construction and rent a small room in an apartment.

But he gets only a few days of work a week, and his work permit is valid only until May 2025. His goal is to get a green card, which would relieve him of the fear of eventual deportation and give him the time to return to his former profession.

“God willing, I have to work on it, I will get my residency,” Mr. Alayón said through a translator. “It would be an honor to be a citizen of this city and the United States that gives us so much opportunity.”

But New York City is not the best place to be looking for a job. The unemployment rate is 5.4 percent, significantly above the national average. Many positions typically occupied by immigrants, like those in hotels and restaurants, never fully rebounded from the pandemic. That has forced people into jobs like food delivery, with low barriers to entry but much competition.

And the push for work permits for the newest arrivals has generated some resentment among the millions of undocumented immigrants who still have no path to legal employment authorization.

“You need to make sure you’re not pitting them against each other,” said James Parrott, the director of economic and fiscal policies at the New School’s Center for New York City Affairs. “I do think over time it will be a positive thing and they’ll be integrated, but in the short run it’s very disruptive and people shouldn’t be blasé about it.”

Dr. Parrott said it would help if state governments facilitated relocation to smaller cities where housing is more available than in the big cities where buses from Texas have unloaded. Some migrants have found their way to other places, often with the aid of a free bus ticket, but it’s not always clear what resources and opportunities await them.

Even for those who have landed a steady job, work permits are a temporary solution while asylum courts remain swamped with applications that now take years to adjudicate, subjecting applicants to perpetual uncertainty.

Yusuf Ali Sendil’s experience offers a view into what the future could look like for millions of newer arrivals with tenuous permission to stay in the United States.

A psychiatric researcher from Turkey, Dr. Sendil said he lost his job for political reasons in 2017. He landed a postdoctoral fellowship at Harvard University on a research visa, and later applied for asylum. Long processing times for an initial work permit forced him to delay his start as a medical resident at Rutgers.

Because that permit lasts only two years, he has already applied for a renewal. But although initial work permits are now coming quickly and last five years for some categories, renewals often take 16 months, according to federal data.

That means Dr. Sendil could face another period without work authorization, which is potentially disruptive to his patients and could derail his career.

“If I don’t get it in time, I lose my job, and if I do not finish my residency, I cannot apply for jobs,” said Dr. Sendil, a member of the Asylum Seeker Advocacy Project, which represents hundreds of thousands of people in similar situations. “All my colleagues are planning for positions after their residency, but I really cannot do that because I don’t know what’s going to happen.”