Hi there, Katie!
The Cast Members involved in Disney Dining are more than willing to work with Guests who want to dine at a particular restaurant, but they must abide by fire codes, occupancy restrictions, and so on. To that end, reservations are generally made in advance in order to keep numbers accurate,
My advice to you is to keep calling (407) WDW-DINE -- literally, once or twice a day. You might find an opening due to a cancellation or a rescheduling.
And if that does not pan out, definitely head to the restaurant podium on the day you want to dine at
1900 Park Fare in Disney's Grand Floridian Resort. It is quite possible to get a same-day seating.
Be persistent and diligent, and you might be pleasantly be surprised!
See you later celebrator,
-Deborah B.