I'm surprised Jayco stopped putting spares on the Greyhawk line. Our 2009 came with a rear bumper mounted spare that we removed and put under the back bed. At that time, some of the Greyhawk Motorhomes had spares mounted under the chassis, between the frame rails.
I wouldn't chance driving more than a couple hundred miles from home without an inflated spare. I'd worry about it the entire trip. At the very least, get a tire without the wheel. Hopefully road side assistance will be able to swap tires. Some may charge extra to swap a tire.
-Michael