I know when we stayed at the Beach Club in December, they had a breakfast service in the bar in the lobby. They had danish, bagels, muffins, etc. and coffee, tea and juice. Typical Disney prices ($2+/bagel, etc.).
You can get a quick lunch at Hurricane Hannahs, but one day of our trip it wasn't open at all! And it was a Saturday! I guess because it wasn't that warm out, they don't have it open all of the time...
You could always walk over to the Dolphin; Tubbi's is open 24 hrs a day.