No, no car rentals near SSR but other options are:
Dollar, Alamo, National have locations at some of the hotels along Hotel Blvd which is "sort of" walking distance from SSR
At the Dolphin Resort which you could get to by taking a bus to Epcot then walking to it or by boat through the International Gateway entrance to the World Showcase.
There are Car Care locations, one near the Ticket Transportation at Magic Kingdom. I believe Alamo is there.
Use a travel website, Expedia, Orbitz, Yahoo to search using SSR's address. They may give you an idea of locations and which Car Rental companies are available.
Good Luck, Beth