Most Residence Inns have 4 pm (1600) cancellation policies. The Marriott on Canal Street in New Orleans has a 3 day cancellation policy. The Orlando World Center Marriott has a 2 day cancellation policy. Resorts tend to require more notice than this. It basically depends on the location and probably somewhat on the size of the property. Business needs dictate that these hotels have to be full or near capacity. The World Center Marriott, with 2000 guest rooms, may need that 48 hours to resell it's cancellations for a given night.
And by all means, watch out for those "advance purchase" non-refunable rates, especially when booking online. Make sure you know what you're selecting when booking.