You did not say which restaurant it is, but you cannot get into a Disney-operated restaurant or any restaurant located inside a theme park by calling the restaurant direct. Those restaurants book exclusively through the Disney dining system. They will not take reservations by direct phone.
If you're talking about a Downtown Disney or Swan/Dolphin restaurant you may have better luck. In fact, it's suggested that you call T-Rex directly, maybe Rainforest Cafe too. You can find the numbers if you run the restaurant name through a search engine like Google. Make sure you are tracking down the Orlando number, some of these restaurants have branches in other cities.