Resort restaurants have always been good to me in this aspect. I have gotten same day ADR's at: Kona's Shutters at CBR, Cape May and a few others. Also some of the places in Epcot: Nine Dragons, San Angel, Marrakesh and Biergarten were all available when I called the day of last December. What I do when I am faced with this last minute thing is I call Disney Dining and tell them what park I want to eat at and they will look and see what they have. They will also sometimes make suggestions of nearby resort restaurants. Most character meals, Le Cellier, O'Hana and a few others are notoriously hard to come by last minute. But then there are always cancellations. I think even though its close you will be able to get adr's if you are flexible on times and locations. Good luck!
P.S. I am so glad this worked out for your husband to get this time off! Have a really fun time!