I don’t think it will take that long at least to get the case in front of SCOTUS. A challenge can be triggered by several things. Governors could interpose and refuse to allow its citizens to be subjected to the mandates or any provisions requiring state funding. Yes, this would take some stones, but if enough Governors got together in a region, say the mountain West, Texas and the plains, this would be quite formidable and require some sort of resolution to avoid the use of force. If more states pass statutes and amendments prohibiting mandates, SCOTUS would feel more pressure. If a constitutionally minded president in 2013 issued executive orders rescinded the mandates, I believe that a challenge to the orders would be very quick.
SCOTUS is comprised of 9 fallible humans beings that respond to events just like the rest of us. They are not stoic Vulcans, immune from political pressure. They may endeavor to stay above politics when deciding the case, but they still respond to the political pressure when deciding to take the case. SCOTUS won’t watch the country burn because they have some compelling notion that burning questions must be given time to bake.
Well, if they screw this one up, they just might watch the country burn anyway.