According to the conceptual proposal released by Senators Menendez, Reid, and Schumer yesterday, the immigration reform to be taken up by Congress would require that
a green card will be immediately available to foreign students with an advanced degree from a United States institution of higher education in a field of science, technology, engineering, or mathematics, and who possess an offer of employment from a United States employer in a field related to their degree. Foreign students will be permitted to enter the United States with immigrant intent if they are a bona fide student so long as they pursue a full course of study at an institution of higher education in a field of science, technology, engineering or mathematics. To address the fact that workers from some countries face unreasonably long backlogs that have no responsiveness to America’s economic needs, this proposal eliminates the per-country employment immigration caps.
How does this affect math? Does it change the visa status of our Ph.D. students? Is a postdoc an “offer of employment,” and if so, will non-U.S. graduate students be eligible to receive NSF postdocs, given that they’d become permanent residents upon taking up their position?
Quomodocumque 
And what does the new Arizona law mean for universities in Arizona? If I were a noncitizen and were thinking of going to a university in Arizona, I’d certainly think twice.
It is too early to tell if this will pass unmodified or at all. Things are likely to change. But if this exact proposal were to pass I could see huge repercussions.
Currently most foreign PhD students come with F or J visas which they can then change (not automatic for J) to an H visa and work for a time. They can stay, but is a laborious process depending on the goodwill of an employer (research math depts usually have the goodwill, others vary).
With this proposed change you will see many more people wanting to come and, I predict, people willing to come without support and to pay tuition for a shot at a green card. I am sure some depts would take advantage of it.
For academia, I think this could be a nice practical boon to all involved, but I don’t think it would change much fundamentally. With the typical visa that PhD students have, they can usually stay and work in US for a year after graduation by taking “OPT status”, which I think stands for “optional practical training”. As Felipe says, if someone gets a postdoc in the US, the university will work with them to get an H visa for that period before the OPT runs out. I think this costs the university some money ($1k?) and the postdoc a lot of time and paperwork.
Outside academia, I think this could have a larger impact. Also, as Felipe points out, it might lead to more applicants to our graduate programs…
This reminds me of Brian Conrad’s letter in the NYT ten years ago.
http://www.nytimes.com/1998/08/27/opinion/l-census-fight-isn-t-about-accuracy-555371.html
Oops. I meant to post the previous comment in the discussion on the census.
I think one thing the government could have done is to extend the F visa from one year to more years (according to the study plan of the international students), this could have saved a lot of meaningless paper work and time. I don’t see much hope in passing the proposal to give instant green card to PhD graduates, it seems too much. Not that I don’t want them to be passed, it just seems to be hopeless at this point.
I wish that they would replace “institution of higher education” by “non-profit institution of higher education”. This sounds like a scam in the making.
http://thepienews.com/news/australia-student-visa-fraud-time-high/