By MIRIAM JORDAN, The Nedw York Times

LAGUNA NIGUEL, Calif. — The delivery trucks began arriving with their precious parcels before daybreak Monday, lining up before the massive ziggurat that rises here above Orange County’s suburban sprawl.

Each truck carried two workers because of the volume of thick envelopes they had to unload. One UPS driver said his truck held 3,000 of them, 10 times the number he normally delivers to the building, a government processing center.

Andrew Langyo, a FedEx courier whose truck was first in line, swung open the back of his truck for inspection by the guards. There were 15,000 packages inside.

“We’re loaded, and we have more trucks coming,” said Mr. Langyo, who would return two hours later in the same truck with another haul.

Last Monday, the starting gun went off on application season for skilled-worker visas, known as H-1B visas, which allow American employers, primarily technology companies, to bring in foreign workers for three years at a time. For the last few years, the government has been so overwhelmed by applications that it has stopped accepting them within a week of opening day — hence the line of trucks trying to deliver their cargo of H-1B applications before the doors close on the program for another year.

And this year, the rush has escalated to an all-out scramble because the H-1B program’s future is unclear. Hailed by proponents as vital to American innovation, the visa program’s detractors say it has evolved into a scheme to displace United States workers with cheaper foreign labor. President Trump has vowed to overhaul it and lawmakers from both parties have drafted bills to alter it.

At his campaign rallies, Mr. Trump introduced laid-off Americans who had been asked to train their foreign successors at companies including Disney. “We won’t let this happen anymore,” he thundered in one stump speech about the practice, which he has deemed “outrageous” and “demeaning.”

Just this past weekend, United States Citizenship and Immigration Services announced a technical change that could make it harder for entry-level programmers to receive the visas, and on Monday, the Justice Department warned that it would investigate companies that it believed had overlooked qualified American workers.

“The Justice Department will not tolerate employers misusing the H-1B visa process to discriminate against U.S. workers,” Tom Wheeler, the head of the department’s civil rights division, said in a statement.

Each year, 65,000 H-1Bs are made available to workers with bachelor’s degrees, and 20,000 more are earmarked for those with master’s degrees. They are attractive not only to the companies that file the applications, but also to the workers themselves, who can become eligible for a green card while working on an H-1B.

Last year, the government took in 236,000 applications in the first week before deciding it would accept no more. A computer randomly chose the winners.

The average H-1B petition, a collection of forms and documents attesting to the bona fides of a job offer and the person chosen to fill it, is about two inches thick. But some files are six inches fat and weigh several pounds, according to Bill Yates, former director of the Vermont Service Center, which also processes H-1B applications.

Mr. Yates recalled some mishaps, like the time a driver bound for the center in Vermont drove 50 miles unaware that his truck’s back door had swung open, spilling its cargo onto the road.

Among the petitions expected to land in California’s center on Monday is that of Minh Nguyen, a software-design engineer from Vietnam who was sponsored for an H-1B by BitTitan, a cloud software company based in Kirkland, Wash. It is his second attempt at a visa.

“In America, you’re in the center of new technology and cutting-edge changes in the I.T. industry,” said Mr. Nguyen, 25. “I would contribute directly to the company and to software development in the U.S.”

In 2014, the last year for which information has been published, just 13 outsourcing firms accounted for one-third of all granted visas. The top recipients were Tata Consultancy Services, Infosys and Wipro, all based in India.

The companies, which subcontract their employees to banks, retailers and other businesses in the United States to do programming, accounting and other work, often inundate the federal immigration service with tens of thousands of H-1B applications.

BitTitan, a growing firm that hopes to hire 60 engineers in the next 12 months, is submitting just six applications. “We are trying to fill specific positions around cloud and artificial intelligence,” said the company’s chief executive, Geeman Yip. “If we can’t fill them, our innovation suffers.”

Mr. Yip opened a small Singapore office four years ago in part to address the worker shortage.

“I want to invest here,” said Mr. Yip. “I can’t be stifled by a shortage of people.”

Several bipartisan bills pending in the Senate and the House seek to make companies give more priority to American workers before they fill jobs with H-1B visas. They also seek to raise the minimum pay for the jobs, which depend on skill level and location — a computer systems analyst in Pittsburgh, for example, must make at least $49,000 under current regulations. The theory is that higher pay would make those jobs more competitive with American-filled positions and eliminate some of the rationale for importing workers.

A draft of a presidential executive order on “protecting American jobs and workers by strengthening the integrity of foreign worker visa programs” was distributed widely in late January but never signed. But without warning over the weekend, the United States Citizenship and Immigration Services published a memo on its website that could affect many applications. The measure appears to be directed specifically at outsourcing firms but could hurt other companies.

Specifically, companies seeking to import computer programmers at the lowest pay levels will have to prove that the work they perform qualifies as “specialty” labor, which is what the H-1B visas were created for. “There will be greater scrutiny of the role the company wants to fill,” said Lynden Melmed, a lawyer in Washington and a former chief counsel for the immigration service.

Even before the change, fears about the future of the H-1B program were making this year more pressure-packed than most. “Just to make sure the petitions get in, almost every client demanded that theirs arrive on the first day,” said Greg McCall, a lawyer at Perkins Coie in Seattle who prepared 150 applications.

FedEx and UPS trucks came and went all day long, as did some smaller delivery companies that received a piece of the action. At 9:20 a.m., one courier, Fernando Salas, pulled up in a red Suzuki station wagon stuffed with 10 boxes. “I have 109 envelopes,” he said. “That is all that fits in here.”

Apo Kelyan of On-Time Messenger Service pulled up at 6:21 a.m. in a van. “This is the busiest day for us,” said Mr. Kelyan, as he carried a load into to the building’s mailroom. He could not stop to speak any longer. “I have to run,” he said.