My cash rewards were carried over from 2007 into 2008. However, I do know that this rewards program's terms & conditions varies. My rewards never expire, and some cardholders' rewards expire after 2 or 3 years. So, it could be true that some account holders' cash rewards zero out after December 31st.
The rewards will carry over on what you have earned. Jan 1 starts the new cap of 300 dollars that can be earned for the year.
That's also my understanding of this rewards program.