Outside Albany, N.Y., where hundreds of recent migrants have been bused upstate from New York City, David Buicko sees an obvious solution to the labor shortage he and other employers are experiencing.

“I’d hire probably 20 people tomorrow,” said Mr. Buicko, the president of the Galesi Group, a Schenectady-based developer, who said prospective workers are still waiting for legal authorization. “It’s crazy that we can’t fill a void, we don’t have population growth, and we’ve got people that we’re just bringing in, sitting around doing nothing.”

Mr. Buicko is not alone. Across the state, many large and small employers have expressed an overwhelming willingness to hire recent asylum seekers; migrants are even more eager to work.

But bringing the two sides together is far harder than it might seem.

Migrants are prohibited by federal policy from securing work permits until 180 days after an asylum application is filed — a process that has resulted in monthslong backlogs and has frustrated both business and elected leaders, especially in upstate New York, where farms and small rural towns mix with a series of often hard-strapped Erie Canal cities.

Congress has seemed unwilling to change the 180-day policy; President Biden has not indicated whether he will take other steps so some asylum seekers can apply for a work permit sooner.

The influx of roughly 110,000 asylum seekers in New York City from the southern border has caused logistical, financial and political headaches for Democrats everywhere, but especially in New York, where it has divided leaders in the usually liberal state and put them in conflict with Mr. Biden.

The same tensions are evident across the nation, including in deep-blue enclaves like California, where buses of migrants have arrived from Republican-led states, and Massachusetts, where the governor and federal elected officials have begged the Biden administration for robust action.

Those calls have been amplified by the private sector: Late last month, more than 120 business executives, including Jamie Dimon of JPMorgan Chase, sent a letter to Mr. Biden urging him to fast-track work permits.

The same sentiment is shared by business leaders in upstate communities in New York, which have seen work forces slowly drained by decades of out-migration, a trend that was often accelerated and exacerbated by the pandemic.

Robert Duffy, a former lieutenant governor who now leads the Greater Rochester Chamber of Commerce, estimated that his city has about 6,000 open jobs, many in service industries like landscaping, manufacturing and hospitality. He noted that some factories and restaurants have cut hours because of lack of labor.

“If you want to work and you’re willing to work hard,” he said, “the opportunities are there.”

The view is largely the same in Lake George, the tourist-friendly Adirondack town that already uses a large, seasonal foreign-born work force on H2B visas for temporary workers. “Our destination is used to working with international workers,” said Gina Mintzer, the executive director of the Lake George Regional Chamber of Commerce. “There are definitely jobs for immigrants.”

Still, there are also pockets of opposition, both personal and political, to hiring the new migrants. Ray Dykeman, a dairy farmer in upstate New York, acknowledged that he simply could not run his business without migrant laborers, who have long fed his cows, cleaned their stalls and worked their way into his heart.

“They’re absolutely phenomenal,” Mr. Dykeman said. “They’re friends and family.”

But asked if he would take on a group of recently arrived asylum seekers, Mr. Dykeman was dubious.

“Do I want to take a chance on a bunch of people that they just trucked in?” he said. “No.”

The migrant crisis — which Mayor Eric Adams warned this week could lead to New York City’s demise — has similarly alarmed voters: A recent Siena College poll showed that four out of five New Yorkers consider the migrant issue to be a serious or very serious problem, with a majority suggesting that officials should work to “slow the flow” into the state.

Assemblyman Chris Tague, who represents a district west of Albany, said that many farmers in his district harbor grudges against Democratic lawmakers for their perceived hostility to the state’s agriculture industry.

“The government makes it so hard for us to manage and fall within the regulations, and now all of a sudden, they just want to throw these folks to us,” said Mr. Tague, a former dairy farmer, adding, “You want us to come in and save the day.”

In New York City, the job outlook is complicated, muddled by an uneven recovery from Covid; the city’s unemployment rate remains above the national average and still higher than before the pandemic, especially among Black residents.

But some sectors of the city’s economy, such as restaurants, have roared back to life, reaching prepandemic job levels. Home health care has seen explosive growth: There are 57,000 more home health care aides in the city today than before the pandemic, according to state data.

Tourism has also largely bounced back, said Richard Maroko, the president of the Hotel and Gaming Trades Council, a hotel workers union.

“You have an industry across the country that is desperate for workers and a potential work force that’s desperate for work,” Mr. Maroko said. “And the only thing keeping them from solving each other’s problems is the federal restriction on migrants working.”

Restaurateurs such as Danny Meyer, best known for founding Shake Shack, have stood beside Mayor Adams and Gov. Kathy Hochul to clamor for expedited work permits, saying restaurants were struggling to find cooks, dishwashers and bus boys. Immigrants have long formed the backbone of the industry, filling jobs that don’t necessarily require English or previous experience. They often work off the books, which could bring owners into legal peril.

“Restaurant owners are prepared to hire them, but they want to do it lawfully,” said Andrew Rigie, the executive director of the New York City Hospitality Alliance, a trade group. “Clearly, there’s not enough Americans that are filling the available jobs, and migrants that are seeking asylum want to work.”

Other business leaders concurred. Kathy Wylde, the president of Partnership for New York City, the business group that organized the letter to Mr. Biden, said the crisis has “reached a point where it’s not just a humanitarian crisis, but a real threat to the city’s fiscal and economic condition.”

Some were more blunt. “It’s just stupid,” said Heather Briccetti Mulligan, the chief executive officer of the Business Council of New York State. “I mean, we’re paying for them to sit in hotel rooms when they want to work. We have jobs that need people, and we can’t match them up.”

Without work permits, many recent asylum seekers have begun seeking jobs and informal gigs in the so-called underground economy, where they may be more susceptible to lower wages and exploitation. Employers may be fined for hiring people without proper work authorization, but enforcement is relatively lax.

Jorge Rodríguez, 39, came to Manhattan from his home in Maracay, Venezuela, last year, with $100 in his pocket, having trekked through the infamous jungle stretch between Colombia and Panama known as the Darien Gap. Since then, he’s been able to find odd construction jobs, commuting to work to Staten Island and installing new wooden floors, making closets or building swimming pools.

He earns around $150 per day, enough to send money home and rent a room in New Lots, Brooklyn. Still, he’d like to work more — and legally.

“Without papers to work, you can’t grow much,” he said. “Sometimes, if they offer you something better — or where jobs are needed — they ask for papers and without that, people take advantage.”

Late last month, Ms. Hochul said she would spend $36 million to assist with migrant case management in upstate New York, noting possibilities for agriculture jobs — an idea that the New York Farm Bureau has backed, while noting it was “a temporary Band-Aid for a greater problem that must be solved in Washington.”

That idea may nonetheless appeal to people like Gregorio Velasco, 40, a middle school physics and mathematics teacher in Bogotá, Colombia, who fled a gang of drug dealers to come to the United States. Currently working — off the books — in the city, he says he would consider coming upstate for a farm job.

“I am originally from the countryside, I know about milking cows, plowing the land,” he said, adding he would like to leave a makeshift tent shelter he’s staying at on Randall’s Island. “I would prefer a more permanent job working in the fields than a delivery job being exposed to all the risks here in the city.”

For his part, Mr. Dykeman says he feels deeply connected to the immigrant laborers on his farm, about 40 miles west of Albany, where he built a soccer field for those workers to use when they aren’t milking and feeding his cattle. He says he’s not sure if other farmers would hire asylum seekers, but his mind seems made up.

“It’s just not going to work for me,” he said. “I want to stick with the people that I got there.”

Raul Vilchis contributed reporting from New York City.