It's early for that sort of panic. But I would say that if you have all you money in one bank, it might be a good idea to move part of your savings account to a different one. The way things are going it would surprise me if we don't loose a bank or two along the way.

I'm not worried about the FDIC failing to cover the money, but the FDIC can take quite a while to get your money to you. If you loose access to your checking, savings and your bank issued credit cards all at once and need months to get it back, it can wreck your life.