I guess it depends on how you define a "bit less than supply." Using the most common definition of STEM jobs, total STEM employment in 2012 was 5.3 million workers (immigrant and native), but there are 12.1 million STEM degree holders (immigrant and native).
Despite the economic downturn, Census Bureau data show that, between 2007 and 2012, about 700,000 new immigrants who have STEM degrees were allowed to settle in the country, yet at the same time, total STEM employment grew by only about 500,000.