But Smith, perhaps recognizing the difficulties of raising the contentious visa cap, offered an alternative that would make more H-1B visas available to tech firms while cutting the number of professions that could apply for the visas.

About are used by technology companies, but there's a long list of other industries that use it as well, to hire fashion models, pastry chefs, dancers, social workers and photographers, Smith said.

Smith said he's "not sure" whether some of those non-tech occupations "are as crucial to our success in the global economy as are computer scientists."

He suggested that some of the occupations no longer be eligible for H-1B status, which would potentially increase the number of visas that would be available to tech firms.

"If Congress doesn't act to increase the H-1B cap, we may need to examine what sort of workers should qualify for the H-1B visa," said Smith at a hearing held today by the House Subcommittee on Immigration Policy and Enforcement.