I was there on Sunday, 3rd, and made it fine with my 19" 255/50R19 all-season tires. However, I drove extremely s-l-o-w-l-y and drove around anything sharp I saw. Took a long time to go those 17 miles.
At the top I saw two people changing their tires: A Jeep Compass and a Volvo SUV. Didn't see anyone else with flats, or stuck on the side of the road, but then, wasn't there all day or anything.
Two Mercedes sedans passed us heading out while we were heading in, and a number of other non-4x4 cars were present in the parking lot. All the vehicles with true offroad tires were, of course, flying.
Interesting: We left around 5:30 (gate was to close @ 6:00), and awhile later 2/3 of the way down the road, an emergency vehicle (think it was fire) and an ambulance passed us heading inbound.