I don't think you will have any problems not having a car, you will just need to plan a little we going off site.
We stayed at Animal Kingdom lodge in 2008 and didn't get a car. The year before we did get a car and found that we got a lot more done.
Having said that, we hadn't really planned for not having a car and thought that we would be alright with the Disney Transportation, which was great for getting around disney, butwhen we wanted to go to Universal for example we got a bit stuck
As mentioned a few times on this thread the Lynx Buses are invaluable, but try and plan in advance so that you can get your bus changes right.
We tried going to one of the malls and because we didn't have the bus time-tables before we set off that day, we ended up having to wait 50 minutes in the scorching heat for the linking bus. It took us 2 hours to get there.
Try and pick up as many of the bus schedules that you can and have a good look at them before you do your journey. Boring i know, but if you put a little time into doing that and you will be able to so much more than just winging it on the day like we did for the first few days .