You might have a tough time getting a ressie but be persistant.
When I was trying for last minute ressies, I called the dining number and told the CM: "Look, I know this is last minute but tell me what you have available on such and such a day around 6:00 p.m." She went through and told me every place that was open for that time.
Of course it does help if you can narrow it down a bit. If you know you want to eat at the park you are in or a certain day, tell the person that.
Have a great time!