This all has to be spun the right way.
I do wonder, if conditions were poor enough and physicians got pushed far enough to unionize, would the powers that be take the threat of a strike seriously at that point? We'd need to show why physicians were forced into a point of needing to defend themselves. Hire some real suave marketing drivers.
If we can get the public on board with the Union move, maybe we can turn public pressure onto the powers that be (Hosp/corp/.gov) so that if the word strike is even mentioned, the hysteria from the public comes crashing down on them, not the doctors. And the ensuring fear from "them" bends their wills to the otherwise reasonable demands of the docs.