It's not really "unheard of". Air traffic controllers, employed by the FAA, famously went on strike in the early 80s and were subsequently all fired by the Reagan administration.
In this case, honestly I'd be like "fine, go ahead and try insubordination, and then get fired." As this article makes exceedingly clear, it will be much easier to continue air travel without air marshals than without air traffic controllers, and the US govt still managed that situation pretty decently.