SAN FRANCISCO — What do computer programmers and illegal immigrants have to do with each other?

When it comes to the sweeping overhaul of the nation’s immigration laws that Congress is considering this year, the answer is everything.

Silicon Valley executives, who have long pressed the government to provide more visas for foreign-born math and science brains, are joining forces with an array of immigration groups seeking comprehensive changes in the law. And as momentum builds in Washington for a broad revamping, the tech industry has more hope than ever that it will finally achieve its goal: the expanded access to visas that it says is critical to its own continued growth and that of the economy as a whole.

Signs of the industry’s stepped-up engagement on the issue are visible everywhere. Prominent executives met with President Obama last week. Start-up founders who rarely abandon their computers have flown across the country to meet with lawmakers.

This Tuesday, the Technology CEO Council, an advocacy organization representing companies like Dell, Intel and Motorola, had meetings on Capitol Hill. On Wednesday, Steve Case, a founder of AOL, is scheduled to testify at the first Senate hearing this year on immigration legislation, alongside the head of the deportation agents’ union and the leader of a Latino civil rights group.