They can and they will make some highly publicized examples of some people in order to terrorize the rest. It is a time-tested practice for imposing rule over the masses.
Wholesale firings will happen too. Once. A group of blacklisted employees will target a convenient executive of the organization that does this and no other organization will try it.
There will be vicious persecution of a few dissidents under newly enacted "Hate Speech" and "Misinformation" regulations.
As the deaths and injuries from the mRNA treatment continue to accumulate the "mandates" for such treatments will become irrelevant. They will not be rescinded, they will simply remain unenforced.
The rumors are unemployment benefits will be canceled if you are fired for not getting the jab.
Interesting stand off developing. Seems a lot of airlines stopped the mandate, but as connected as they are to the .gov that won’t last long.