President Barack Obama said he may use executive authority to make it easier for individuals who enter the U.S. on an H-1B work visa to remain in the country. Republicans immediately countered that the program, aimed primarily at tech workers, is already costing too many American jobs.

Noting that he previously signed an executive order that allows foreign youth to remain in the country regardless of their parents’ immigration status, the president said he may use his pen to reform other parts of the system.

“And that includes potentially making the H-1B system that is often used by tech companies and some of the other elements of our legal immigration system more efficient, so we can encourage more folks to stay here,” said Obama, who spoke last week at startup incubator Cross Campus in Los Angeles.

The White House released a transcript of Obama’s remarks Friday.

The U.S. government awards a maximum of 85,000 H-1B visas annually. Workers on the visa are typically required to leave the U.S. after six years unless they can transition to permanent resident, or “green card” status. Current laws make that transition difficult for those who do not already have family in the country.

Over the weekend, Senator Charles Grassle, R-Iowa, released a statement accusing the president of being insensitive to the plight of tech workers whom Grassley said have lost their jobs because of competition from H-1B workers.

“Acting unilaterally for some businesses without providing protections for U.S. workers would be detrimental to the future of the workforce,” Grassley wrote. The senator, who would become chairman of the Judiciary Committee if Republicans carry the Senate in the November midterms, said tech-industry layoffs were up 68 percent in the first half of 2014.

Grassley suggested that the H-1B program should be amended to require employers who bring in foreign workers to prove that there are no Americans able to do the job. “All employers, not just some, should be required to offer the job to a U.S. worker who is equally or better qualified,” said Grassley.

Such a reform could place a considerable administrative burden on companies that are heavy users of the H-1B program. IBM, Microsoft, Amazon and Google were among the top 20 H-1B users in 2013, according to an analysis by Computerworld. Indian outsourcing firms that place workers in the U.S. on behalf of clients were also heavy users.

Critics of the H-1B program argue that it is rife with abuse. Some point to Concept Schools, an Illinois-based operator of charter schools that has used H-1Bs to import more than 400 K-12 teachers over the past several years — virtually all of them from Turkey, into districts where unemployment among educators is high. Concept is operated by followers of controversial Muslim cleric Fethulla Gulen.

“Contrary to what most people believe, including most policymakers, it is extremely easy for an employer to avoid hiring qualified American workers when hiring H-1B workers. American workers often do not have the first and legitimate shot at these jobs,” said Ron Hira, a professor of public policy at Howard University in Washington, D.C. and a longtime critic of the H-1B program, in an email to International Business Times.

With his call to make it easier for H-1B workers to remain in the U.S., Obama risks splitting his base. Silicon Valley billionaires and millionaires like Google’s Sergey Brin and Yahoo’s Marissa Mayer are big donors to the Democratic National Committee and also support expansion of the H-1B program. Organized labor, a traditionally Democratic stronghold, would like to see the program reined in.