It's at least worth checking to see if you can find any discounted rates / codes for a car rental. You should be able to find a weekly rental for under $200 somewhere.
Other things to consider:
Grocery Stop - Whether you rent a car or obtain other transportation, consider an option that will allow you a stop at a local grocery store. If your budget is important to you, you can really save a bundle by purchasing simple things like soda, bottled water, breakfast items (pop tarts, granola bars) and snacks (potato chips, cookies, etc.) at a grocery store instead of WDW. I believe that the beverages alone will cost you $2.50 each at the resorts and theme parks. Think of how much you can save by picking up those items when you arrive and keeping them in your room.
Some town car companies, and I believe
FL Tours is one of them, will allow you one stop of 30 minutes or so to pick up these types of items. If you get a rental car, you can go whenever you wish.
Souvenirs - If you have a significant souvenir budget, a rental car would allow you to get to some of the off-site outlet stores that often have WONDERFUL discounts. We've gotten t-shirts, sweatshirts, polo shirts and other items for 50-75% off the prices you see at WDW itself. These are the same items sold at the theme parks, but have been moved to the outlets because designs have been discontinued, or some other reason. We bought a t-shirt for our son that read something like 'my first trip to Disney World'. We paid $4 for the shirt at the outlet, and the rest of our trip saw the exact same shirts at the parks and resorts for $12.
Having your own transportation at the parks can also be a benefit. By and large, the WDW busses and other transportation options are very good. But during busier times (first thing in the morning, at a park's closing time) you may find yourself having to wait for multiple busses to arrive before there is room to board. The last few times we were at WDW, we either drove (and had our own car) or rented a car. Typically the only park to which we will consider taking the bus is the Magic Kingdom since the bus drops you off so much closer than the parking lot.
And, since you're staying at a WDW resort hotel, self-parking is free throughout the complex.
