We met a couple from Washington, DC who rented an Alfa Romeo from Budget and went for a few laps
His brakes were shot at the end. The rental car places actually list the 'Ring as a place you cant go, but as you all know there is no faster car than a rental car. A few years ago I took a 5.0 Mustang around Texas Motor Speedway that I think was from Hertz or Avis.
As you get ready to plan your trip have a look at this
http://www.nurburgring.org.uk/
Great information from a group of guys who go all the time.
Flights are cheap to Europe Oct-Mar, I come over to the US every couple of months and just booked to go to Boston from Manchester for 252 GBP about 500 US.