Try calling the restaurant directly. They release very few reservations to Disney, and save most for direct calls. If that doesn’t work, I wouldn’t worry too much. I don’t think you’ll have issues with a walk up if it comes to that.
We waited less than 20 minutes for a table for 2 as walk ups during a very busy time when no reservations were available. I’ve never had problems getting a table, even on the same day. I think we’ve only ever made a reservation months in advance one time. Every other time we’ve made the reservation anywhere from the same day or the day before to a week out, and we’ve always gotten a table.