Ken - correct me if I am wrong, but Bank's are not required to be open on Saturday. With sufficient notice, they could choose to close that day.
I could not answer for all 50 states, but believe if you are state chartered and you are not going to be open on your normal days the state has to say grace over the choice. A client bank closed for the state basketball championship without asking. Not pretty. I don't think closing because you could not figure out how to post the day's work would be any smarter.
P.S. The basis for any such rule would be fear over bank closures, vis a vis the 1930's.