The answer is somewhere in between, depending as much on new technologies and the U.S. education system's ability to keep up as on the immigration law itself. But the sliver of computer-related jobs inside the U.S. that might be designated for foreigners — fewer than 200,000 out of 6 million — has been enough to strain a bipartisan deal in the Senate on immigration reform, showcase the power of big labor and splinter a once-chummy group of elite tech leaders hoping to make inroads in Washington.

"A lot of people agree that employers should have access to (highly trained) immigrants — that they are a benefit to the country, and we are a country of immigrants," said B. Lindsay Lowell, director of policy studies at Georgetown University's Institute for the Study of International Migration. "I think the question is how much of a good thing is good."

The Senate immigration bill — the result of months of quiet negotiations among eight influential senators — is on track to nearly double the number of highly skilled foreign workers allowed to work in the U.S. under what's called an H-1B visa, from 65,000 to 110,000. The number of visas could climb as high as 180,000 depending on the number of applications received and the unemployment rate.