PALO ALTO — Companies are seeking more foreign workers than ever before to fill highly skilled jobs in technology and other industries, but the United States will grant visas to just a fraction of them in a lottery that began this week.

Anxious to bump up those visa limits, a bipartisan campaign is seeking to make an exemplar of one of the record 233,000 people vying for 85,000 H-1B temporary visas: Belgian entrepreneur Pierre-Jean “PJ” Cobut. If Cobut cannot obtain a work visa before his student visa expires in June, the co-founder of Palo Alto’s Echo Labs said he planned to move his health care device startup to Canada.

Joining the 32-year-old will be his Israeli co-founder, Elad Ferber, also waiting for a coveted H-1B visa.

“If it comes down to it, we’ll move,” Cobut said. “We can’t be fighting this battle forever. At a personal level, it’s really stressful and a distraction to running the business.”

The campaign, backed by Silicon Valley tech titans, has launched a website and is promoting a Twitter hashtag called “#LetPJStay” that illustrates his story and others.

But some advocates for welcoming high-skilled immigrants permanently, not just temporary H-1B workers tethered to the firms that recruit them, have said the advocacy is misplaced.

“The number is not a reliable indicator of how many jobs there are,” said former U.S. Rep. Bruce Morrison, D-Conn., an immigration lawyer and lobbyist who speaks for engineers wanting more legal immigrants but fewer H-1B visas. “A huge percentage of these applications are from offshore, outsourcing operations.”

With “absolutely no penalty to overapply,” Morrison said many companies, led by staffing firms based in India, are simply filing for as many foreign employees as they can in order to get a better chance of increasing the share who do get visas. Corporations like H-1Bs, but the U.S. would be better off overhauling the system and giving out more green cards that give immigrants permanent residency, he said.

Others want to go even further in cutting back on the visas they believe displace Americans. A bipartisan group of U.S. senators earlier this month called for an investigation into abuse of the H-1B program after allegations emerged that utility company Southern California Edison was replacing laid-off information technology workers with new hires from India.

But the campaign to increase the number of temporary visas has powerful backing this year from groups such as Michael Bloomberg’s Partnership for a New American Economy, which advertised Cobut’s story, and FWD.us, an immigration lobbying group launched by Facebook CEO Mark Zuckerberg and backed by tech leaders including Microsoft founder Bill Gates, Yahoo CEO Marissa Mayer and Google Chairman Eric Schmidt, all of whom represent companies that recruit a large number of H-1B workers.

On Tuesday, the group sent a dozen immigrant entrepreneurs to join U.S. Sen. Orrin Hatch, R-Utah, as he reintroduced his Immigration Innovation Act, known as I-Squared, in Congress. The bill would increase the H-1B cap to 115,000 and as high as 195,000 depending on economic conditions.

The growth of the technology sector in the late 1990s persuaded Congress to raise the cap to 115,000 in 1999. The limit rose to 195,000 in the new century before dropping back to its current level in 2004. Of 85,000 available visas today, 20,000 are reserved for those with advanced degrees.

“Three out of 10 people have a chance of getting in … or four in 10 if you have a graduate degree, the lowest it’s ever been,” said Todd Schulte, director of FWD.us. “It’s a tragic reminder we have an incredibly broken, outdated immigration system. The last major overhaul we had was 29 years ago, in 1986. Cutting-edge consumer technology was my Atari.”

Cobut, who has a business degree from Stanford University, hopes he gets through the first H-1B lottery round that prioritizes those with advanced degrees. “I don’t know if H-1B is the answer, but I guess it’s an easier battle to pick to increase the quota rather than changing the system,” he said.

Cobut said Silicon Valley remains a beacon of innovation and entrepreneurship that draws talented people from around the world, but “that reputation could change into, ‘It’s a great place if you’re American. If you’re not, save yourself the trouble and go somewhere else.’ “

Contact Matt O’Brien at 408-920-5011. Follow him at Twitter.com/Mattoyeah.