No it is not fixed, it is variable. When SS needs more money, the rate goes up automatically. The fair tax has automatic tax increases built in to cover whatever SS needs. Quite a reform, and I sure people who paid in their whole lives will be happy to know they are still paying these built in SS taxes after they retire.
Apparently, the fair tax ties the SS portion of the rate to reported wages. Currently, wages are under reported because people don't want to pay the SS tax. I take only a small salary out of my business for that very reason. Once the fair tax is adopted, people will report higher wages which will cause the fair tax rate to go up automatically. This will also lead to having the SS being on the hook for paying more out in benefits.