Answer from Randy: Tell them to come back after the bank has time to order enough cash for the customer. You can't get blood out of a turnip.
Answer from Andy: I would tactfully explain to the person that the branch does not keep that much cash (and I assume this is a large check, or the branch is unusually low on cash) and they can either go to your XYZ branch which has an adequate amount, or you will make arrangements to have an extra shipment and would be happy to meet their request on X date. If it is a large check, a common practice would also be to urge them to take a cashier's check for all or part of the amount, or to wire it. These are safety precautions for the benefit of the payee.
First published on BankersOnline.com 3/25/13