I think there might be a dip in prices on the lower end aircraft, since this is what most people that are just flying for fun are more likely to rent. If the loans start getting a little scarce, these customers are probably going to be what shores up the operation until things return to normal.
I suspect there will probably be quite a few twins and high end singles at schools that will just sit because of the high cost of rental. Even if rental rates decrease at the same rate as every other aircraft they own, it still puts them out of the reach of the cash paying customer.
The flying club/school I fly with is already having to shut down operations at one of the airports it is based at, because of a downturn in business and persistent high avgas prices at that airport (~$7/gallon). There were probably other factors as well, such as property and airport taxes, which I understand are some of the highest in the Atlanta area. I haven't asked, but I'm going to assume they'll probably sell off the two 172s and move the DA-40 up to RYY...but we'll see. The instructor I've been flying with says he's getting let go, though he was going to leave in a couple of months anyway to move to Montana.