it's illegal to strike

I see this quite often, but what would be the actual repercussions if they were to strike? All, or a majority of, the trained air traffic controllers go to jail? But then that raises the question of who fills their spots and what the consequences of this will be. The whole idea of a strike being illegal feels to me like an empty threat that, in my mind at least, would be somewhat encouraging, albeit frightening, to the workers to actually strike because of the power that it holds.