I've found some "hard" info to back up what Richard Gentil has been saying.
Flight Training Candidate Checks Program should make interesting reading for prospective students and CFIs.
Note the limited number of schools who are included in the authorised flight training centres. Some of your favourite schools are not in there!!!
Personally I think this is because this scheme is not yet in place, they are moving towards it, this web site is a taste of things to come. I went to two largish flight schools today and they have heard nothing about changes to how they should handle foreign students. They will still take you off the street, take your money off you and train you, and not give a damn about your nationality or immigration status. That is because the rules have not yet been formally changed. The only advice they have had off the authorities is to report anything suspicious. If you are a typical Northern European type they will not have their suspicions raised. Sorry to say it but it's a fact.
I'd get legal advice if you are at all worried. This is not a place to obtain authorative legal advice. If anybody wants to pay $300 then this guy
Shusterman is extremely well regarded. He is nothing to do with me, my brother who is also an US immigration attorney (and who tells me most of what I say - hearsay of course) says this guy is one of the best around.
Note in the FAQs
At this time,US citizens, nationals, and certain aliens are not required to use this program
So reading between the lines, its coming........
sheep guts
This might be of interest to you - a document refering to specific legislation.
Training in aircraft of more that 12500 lbs