When will the Court strike down the vaccine mandate?

They have to finish it first

There has to be a lawsuit first

What are the chances it's just a threat to compell companies to institute mandates? They know they're on tenuous legal grounds so they are trying to bump as many companies over the edge to make them do their dirty work for them.

They won't. Roberts and Kavanaugh will switch

The courts on on "their" side. Don't be surprised if these seemingly illegal mandates are upheld in the name of "public health." That will be the dog whistle to go after guns.