Smith, in a request for comment about Schumer's criticism, sent this response by email: "The STEM Jobs Act narrowly defines what constitutes a research university to ensure STEM green cards are only given to the top foreign students graduating from American universities."

"The STEM Jobs Act does not discriminate against for-profit or online schools but does contain stringent criteria for universities wanting to participate in the new green card program. Universities are only eligible for the program if they have been classified by the widely-respected Carnegie Foundation for the Advancement of Teaching as doctorate-granting institutions with high levels of research activity or classified by the National Science Foundation as having an equivalent level of research activity," Smith said. "This helps ensure that STEM green cards are not just a golden ticket for those wanting to come to the U.S."

Daniel Costa, an immigration policy analyst at the Economic Policy Institute, said, "If the Smith bill would have left the school requirement as only doctorate granting universities with a 'very high or high level of research activity' as determined by Carnegie, that would have been a little bit better than what's actually in the bill."

That amounts to a total of 207 schools, which "way to too many in my opinion to be the elite homes of the best of the brightest," said Costa. But the Smith bill "inserts a loophole" that allows a school to apply to the National Science Foundation for a waiver. A waiver can be granted if the NSF finds the school to have "equivalent research activity to those institutions" that Carnegie has designated, he said.

While Costa believes "it's unfortunate [the] Smith Bill doesn't explicitly exclude for-profit schools" and online programs, he is not sure that it includes them as Lofgren's fact sheet claims. None of the schools among the 207 are private, for-profit schools, but the question mark will be over the NSF waiver process and what that allows, he said.