To confirm and expand on what others are saying: a general strike is not protected, and any union that endorses one will lose their recognition. How can you get that many people to risk their jobs, with no organizing union that can even legally participate?
If you can get that many people that dedicated to your cause, it would be a whole lot easier to just get them to vote in a primary.
Our democracy is deeply broken, but it is a democracy. If we lost it, you'd just get the batshit insane party candidate put directly in, and they could do whatever they wanted.