So...what happens if a team goes over the Salary Cap?
The short answer is simply that NO team CAN go over the Salary Cap. Note that every contract must go through the NFL League Office before the deal can be made official. Presumably, one of the things the league must do at this time is determine whether or not the contract would violate the NFL's Salary Cap. If the deal does violate the cap, then the NFL will reject it.
There have been instances in which a team has managed to sneak a cap evading contract by the league. Upon further review, the violations were caught by the league and the respective teams were penalized. Penalties include fines and/or forfeiture of draft picks. In recent history both the Pittsburgh Steelers and San Francisco 49ers have been penalized draft picks, while the 49ers' front office personnel (Carmen Policy and Dwight Clark) were also fined.
from: Ask the Commish