I don't know for sure about DL, but I'd assume it's the same as WDW.
At WDW you can cancel/book your reservation at any time, including 'same day reservations' as long as there are openings. The thing to remember is that you aren't 'changing' or 'modifying' a reservation, you are completely canceling one and then booking a whole new one. You can't hold on to your existing reservation, book the new one, then cancel the old one. Just be sure to check the calendar first for availability and book the new park immediately as the procedure means you are taking the (hopefully) slight chance that in between cancelling your existing and then going back to the calendar to select your 'new' reservation, the reservation is no longer available. In other words, there is no guarantee so I'd make any change as soon as I could.
That being said, I cancelled three park reservations (not 'day of' though) at WDW and didn't have a problem booking a new park reservations.