Disney policies can be very confusing and/or contradicting in places:
https://disneyworld.disney.go.com/faq/dining-reservations/restaurant-reservation-cancellation/
Rule-of-thumb is 'at least 24-hours', so unless you have a midnight dining reservation, 11:59pm will not work for a reservation the day that begins one minute later.
But I'll give Disney some credit - details are provided when you make your ADR and in the initial 'Confirmation' email, and they send at least one other email prior to that Cancelation-window as a reminder.
Try to make a reservation right now, the 'Guest Policies' you must confirm you've read states:
"Reminders
Reservations must be canceled at least one day prior to....avoid cancelation fee."
So, if a person/family has a reservation for, let's say, any time on Thursday, I would suggest canceling no later than 11:59pm on Tuesday.
Not really two-days, but certainly more than 24-hours.....to avoid the cancelation fee.