You do realize that this is hypothetical? The law, regulation, or order to enact this does not currently exist. So there's no real telling what the consequences might be.
In the landmark case in 1904, there was a fine for not getting vaccinated. "You refuse to do what's necessary to support public health, so we will take money to help pay for the repercussions of your thick-headedness," seems appropriate.
More importantly, I don't think that there will be government-level mandatory vaccinations.
Instead, you will just see continuing "ratcheting up" of the pressure from private parties and regulation to get vaccinated.
On the regulation side, you have NYC just mandating vaccines for indoor restaurants, gyms, and performances (plays, concerts, etc.).
On the private side, you have increasing numbers of employers and venues requires vaccination.
At a certain point, if you want to participate in public life in many states, you will need to be vaccinated- I am sure that universities and schools will have those requirements, you will need it to travel, and so on.
...of course, given polarization, it may be that you will have certain states (FLORIDA MAN RUNS ON METH, NOT MASKS) that push back and pass laws that try to prevent private requirements for masking and vaccination.
Ugh. If someone had said, one year ago, "Hey, there are going to be widely available vaccines for every single person in the US for COVID." I would have been overcome with joy (and, admittedly, somewhat shocked). But if they had told me, "But the problem will be that people will refuse to take them, so COVID will just keep comin' back" I might have cried.
....and schools are starting up. And this is the summer. So very tired of this.