This is a really volatile issue, so it's hard to answer. We really have no idea what changes Team T plan for visa policy.
That said, there are currently multiple bills proposed to muck with the H1b system. Remember, first, that these are BILLS. They need to be passed by both houses of congress and signed by the pres before anything changes, and most bills go through a complex editing process before being passed. So what's in them now may be edited / combined / totally rejiggered. But at present, none of them would change GME all that much. I haven't read the bills myself, all of the following is from online summaries:
ISSA Bill HR 170 - this one would have no effect on GME. It changes the income "cap" where H1b visas are counted towards a total that defines whether an employer is H1b dependent or not. For any employer of >50 employees, 15% need to have H1b's before this happens. Chances of any hospital system hitting this threshold (when you include all employees) is really small, so changing the way this is counted will not matter at all.
The Grassley/Durbin bill will also have no effect on GME. It adds a cap such that no company can have more than 50% H1b's (again, not a problem for a hospital / health system), and changes the way that H1b visas inside the cap are allocated in such a way that would actually benefit GME, but isn't really an issue since most hospitals get H1b's outside the cap anyway.
There are a couple of other bills that have been introduced. Most change the way H1b's are allocated, remove country limits, or prioritize H1b's to employers that pay more than the prevailing wage. Again, as most hospitals get their H1b's outside of the cap (and hence how they are prioritized would be meaningless), I don't think these will have much effect. That I can tell, none of them mandate that H1b visa holders are paid a higher-than-prevailing wage, which would definitely seriously affect GME.
Trump is also (apparently) planning an EO in this sphere. Rumor is that he may change H1b, J1, L1, and OPT visas. No clear details have emerged, and I expect it will just be signed and released without debate as appears standard for President T. Since no details are available, it's impossible to predict effects.
The biggest risks to GME would be changing the cap exemptions for H1b, limits on J1's, or OPT changes. None of the bills sponsored muck with the H1b exemptions for non-profits so far. J1 visas are very complicated because they come in many different flavors -- alien physicians, Au Pairs, camp counselors, and others are all on J visas, so it's possible that one part of the program could be changed leaving the alien physician piece alone. Changes to the OPT program are my biggest worry, to be honest -- simply because any knife (or axe, your choice) that Pres T uses to change the program will affect everyone -- so changes made to "fix problems" in the IT industry may have unintended blow back into GME.
As far as this match is concerned, the biggest problem is uncertainty. I have no idea whether the residents who need visas who are on my rank list will be able to get them or not. I'll need to decide between now and Feb 22 what I will do. As I mentioned in another thread, I don't want to make any changes -- I want to rank people based on merit. But if someone can't start, that has a huge ripple effect upon everyone else in the program, and it's my job to be their advocate. So it's a tough balance.
Last, it will be interesting to see what happens after the match. I could imagine an unmatched US citizen (perhaps a US-IMG) being angry that they did not get a spot, where a non-citizen does. I could imagine that person (or a group of them organized) complaining to someone in Congress. And I can imagine an administration whose mantra is "America First" being upset about the situation. I can see that side of the argument, especially for H visas. H visas are supposed to be for foreign workers where a US citizen can't be found to fill the spot -- so if there is a US citizen, it seems like an abuse of the visa system. If the gov't insists on a change, the match would need major changes. Note that programs couldn't just pull out of the match and take those that need visas -- the same problem would arise.
This debate was going to happen at some time. The growth of US-IMG's and offshore schools was almost certain to create a situation where US IMG's can't find spots, while visa holders can. Once this happens to enough people, or happens to a single person who is important/connected/finds a way to get their story out there, changes are likely. It looks like it's going to happen in the near future. Some change is probably good -- I do think that US citizens should get some priority, or the rules regarding US citizens going to Med School outside the US should be changed (esp Federal Loans). How to do this is the challenge.