But the backers of the program are not giving up, as a new bill introduced this week aims to exempt foreign graduates of U.S. PhD programs from counting towards a cap on H-1B visas.

U.S. Rep. Jeff Flake (R-Ariz.), introduced what he calls the "Stopping Trained in America PhDs From Leaving the Economy Act of 2009 ." By design, the bill's acronym, Staple, represents the stapling of science, technology, engineering and mathematics PhD diplomas onto green cards, granting their holders permanent residency.

Foreign students make up a substantial portion of U.S. PhD graduates. According to a survey conducted by the Computing Research Association, 55.5% of the 1,597 computer science PhD degrees awarded in the last academic year.

There have been a number of efforts to increase the H-1B visa cap apart from a comprehensive immigration reform push. But supporters of an overhaul of the immigration system have managed to stymie such efforts to get Congress to separately consider changes to the H-1B program.