I was looking into this as well and one of the things I discovered was that Scottsdale has a lot of timeshares (Westin Kierland Villas, Sheraton Desert Oasis, Marriott Canyon Villas, Four Seasons Troon North, etc).
While you can rent these directly from hotel companies, and no doubt they will be very expensive for the Superbowl, you can actually rent these directly from an owner and probably pay much less for what you are getting. The advantage is that not only do you get more space (500 sq ft to 1000 sq ft+) you also get a kitchen so you can save on meals.
Some of the websites where you can rent timeshares (with Scottsdale locations) that I found are:
http://myresortnetwork.com
http://timesharerentalvacation.com
http://tug2.com/timesharemarketplace/
http://redweek.com (requires $25 annual subscription to see listings)