The ritual goes like this: If you’re approaching the god Balaji with an appeal, walk in a circle around the temple 11 times and leave an offering of tulsi leaves at his feet. Should your wish be granted, come back and do it 108 times.

“We call him Visa Balaji,” said Madhu Vadlamani, 25. “He is famous for granting visas.”

Vadlamani and her husband of just three days, Revanth Chilakamarri, 29, were but two of thousands of worshipers orbiting the “Visa Balaji” temple near here one ­recent morning. Years ago, the incarnation of Vishnu had blessed them both with student visas to the United States. Though they had grown up just seven lanes apart, they met in America and fell in love.

The two software developers had returned to the temple that morning to appeal to Balaji, in hopes of renewing their American sojourn with a new visa — the H-1B.

For the new political order taking shape in Washington, how­ever, H-1Bs aren’t quite welcome. Amid promises of sweeping changes to immigration policy, President-elect Donald Trump and his choice for attorney general, Sen. Jeff Sessions (R-Ala.), have tabbed the program for a major overhaul, and might even scrap it altogether. In the House, Rep. Darrell Issa (R-Calif.) is on the same wavelength.

The visas bring nearly 100,000 “highly skilled” contract workers, mostly in tech and mostly from India, to the United States every year. Most stay for multiple years, and some eventually get green cards. According to federal guidelines, H-1Bs are intended to fill positions for which American workers with the requisite skills can’t be found. Whether the program always does that is intensely debated by industry lobbyists and politicians, and companies are not legally required to ensure that result.

Trump has described H-1Bs as a “cheap labor program” subject to “widespread, rampant” abuse. Sessions co-sponsored legislation last year with Sen. Ted Cruz (R-Tex.) to effectively gut the program; Issa, a congressman with Trump’s ear, released a statement Wednesday saying he was reintroducing similar legislation called the Protect and Grow American Jobs Act.

Sessions probably will give at least a glimpse of his plans regarding the program at his confirmation hearing Tuesday.

Sessions and Issa’s legislation primarily targets large outsourcing companies, such as Infosys and Tata Consultancy Services, that receive the vast majority of H-1B visas and use them to deploy workers to American companies seeking to cut costs. In 2015, the top 10 recipients of H-1B visas were outsourcing firms. As recently as 2013, the Justice Department, which Sessions stands to take over, settled with Infosys for $34 million in a visa fraud case.

“Logically speaking, I’m worried,” said Vadlamani, who until recently worked for Deloitte in Orlando. “But being Indian, I believe that if it is in my karma, then I will get the visa. If not, there are more and more jobs these days at good companies here.”

But if Vadlamani is circumspect about her prospects should the visa program be restricted, politicians and business executives in her home town are bullish. Not only is employment booming in Hyderabad, they say, but should the United States move against H-1Bs, their economy stands to gain.

The H-1B program provides American companies with cheap, temporary contractors who often work longer hours than Americans and take on the monotonous programming jobs Americans scorn. Proponents of the program argue that foreign workers increase innovation at American companies as well as contribute to local economies. A few Indians who came on work visas have even gone on to become heads of important American companies.

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Meanwhile, India’s growth as a global tech hub has been hampered as tens of thousands of workers have left.

Over the past decade, though, cities like Hyderabad and Bangalore have slowly but surely gained prominence. At first, Hyderabad was mostly a base for outsourcing companies servicing American clients, but now it is home to the biggest offices of Apple, Google, Microsoft and Facebook outside the United States. Amazon, Dell, Uber and others have major operations there. All have huge campuses in a part of the city officially known as Cyberabad.

Cyberabad’s existence is the result of investments in education and infrastructure made by N. Chandrababu Naidu, the chief minister of Andhra Pradesh, where Hyderabad was located until the state was bifurcated in 2014. A network of dozens of information-technology institutes trained a generation of engineers and software developers to work back-end jobs for American companies.

For that generation, getting an H-1B was the holy grail. Even though the work in America could be dull, being there provided a chance to engage with an invigorating culture of innovation that just wasn’t present in India yet. And of course, working abroad meant a huge increase in income and prestige.

But the H-1B cap meant that the bulk of Indian tech workers stayed back. The current cap — not just from India — is 65,000, plus another 20,000 who have graduated from American universities with advanced degrees, down from almost double that at the beginning of the 2000s.

Among those who do get the visas, most ultimately return to settle and work in India. In Hyderabad, many of those returnees are confident that their city can compete with Silicon Valley for India’s brightest young minds.

K.T. Rama Rao, the son of the current chief minister, was one of them. Now he’s the minister for information technology in his father’s government. He pointed to Apple as an example of how Hyderabad could absorb the thousands of workers in a potential future with far fewer H-1Bs — or without them altogether.

“Apple is already moving their maps division here, and they’re doing that because we’re producing more G.I.S. talent than anyone else in the world,” he claimed in an interview, referring to geographic information systems. “Ideally, a president of the United States would have a balanced perspective on business, but if he wants tech firms to stay, he should create better job readiness in the U.S.”

Rao said that legislation targeting big Indian outsourcing companies would wean them away from their dependency on servicing American companies. Without the visa program, they would have to engage in new lines of work that created value in Hyderabad and not abroad, he said.

Amit Jain, now the president of Uber India, is another returnee who used to be on an H-1B. He said that the influx of American companies, as well as a growing indigenous start-up culture, could offer what Indians used to seek in the United States closer to home.

“We definitely have a more robust ecosystem here now,” he said. “We’re seeing plenty of hiring in the future.”

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