SAN FRANCISCO — Sanket Sant, a citizen of India, came to the United States at age 21, earning a master’s degree in engineering, followed by a doctorate and then landing a well-paying job at a company making semiconductor equipment.

Then, he waited for the American government to decide if he could stay.

“I know this country better than my own country, and I still feel like an outsider,” said Mr. Sant, 35, who received his Ph.D. from the University of Texas at Dallas in 2006, and has been waiting for federal officials to approve his green card application for six years. “That’s the thing that bothers me.”

That is also the predicament of tens of thousands of workers here in the heart of the tech industry who were born overseas and educated in the United States. Though not living in poverty or in the shadows, as are migrant workers who are here illegally, they are nevertheless in a bureaucratic limbo while they wait in a long line for a green card.

Now, though, Congress is poised to end their uncertainty.

The Senate Judiciary Committee on Tuesday approved a broad overhaul of the nation’s immigration laws on a bipartisan vote, and sent the measure to the full Senate. The bill would make it much easier for science, math and engineering graduates of American universities to become permanent residents.