For DVC reservations, the Dining Plan must be added to the reservation in advance (typically three or four days prior to check-in -- it cannot be added by the hotel but must be added by Member Services, during normal Member Services business hours). You pay at check-in.
While it may be too late to make reservations for some of the most popular TS meals, I've never read of a case where even the day-of folks were unable to get a TS reservation at some participating restaurant in the parks, hotels or Downtown Disney. As long as you're flexible with regard to place and time, you will be able to be accommodated somewhere.