Not legal advise, just my opinion:
If you are a full time employee, i.e. not an independent contractor, they cannot sack you because you do not have the correct visa to work in a new jurisdiction. If you tell them you cannot legally work in the US and they fire you, they have essentially fired you for not breaking the law. I think you could sue the pants off them. I am not a lawyer but if I was genuinely worried about this in your position, i would definitely seek advise. I feel like there is no chance you an be sacked for not getting: a visa to work in a new jurisdiction, 3 months after you start. They might have had a condition "will work anywhere globally" but the onus is on the employer to get the necessary work visa. How can you be responsible for that?!