I was referring specifically to foreign students here on student visas. They can receice authorization to work while being a student, but they cannot continue working without a change in status. They need sponsorship of a business to stay and work here. The Obama administration and even Bush have facilitated this transition from student to work. In addition to the 65,000 H-1B visa annual cap, there is an additional 20,000 H-1B visas for STEM graduates plus an additional exemption for non-profit organizations. And Obama has issued an executive order allowing spouses of H-1B holders to work.
The bottom line is that there is no shortage of STEM workers. Here is an excellent CIS study on the issue Is There a STEM Worker Shortage?
The proposed TPP will allow foreign companies to import their own workers into the US. Jeff Sessions has written extensively on its impact on our workers.
They may require a “change of status” but they don't require a H1B. A STEM with a B.S. can work full time for 30 months without a H1B, and legislation was being negotiated last year to increase that non-H1B work status to 6 years.
I don't know the specific non-H1B opportunities for STEM Masters Degrees.
But, the Chinese, Indian, etc. STEM PhDs who are still working in the USA five years after graduation do not have H1Bs.
Re: “...plus an additional exemption for non-profit organizations.”
That also includes unlimited exemptions for universities and government agencies of any kind. The Department of Defense can hire and renew exempt H1Bs for up to ten years.
Many universities actually subcontract federally funded research, then hire H1Bs, then staff the subcontractor with exempt H1Bs.