I have two different thoughts on this subject.

 1. The government has no business insuring private companies (like banks).  That just encourages the banks to take more risks because the feedback loop of going bankrupt is non-existent. So in the case where the government is not insuring the bank then we all would keep a better eye on the bank's stability and I would move my money asap.
 2. Since we do have the FDIC, there is no urgency for you to move your money. For one thing your bank might get purchased and you'll never see a disruption of service (happened to me with Netbank being bought by ING).  If a purchase does not happen then the worst case scenario is you have to wait about a week to get a check from the FDIC.  If waiting a week for your assets in this bank would hurt you then you should move your money.