Small spaces suck as photo studios...but sometimes you have to just work with what you have.
When talking about backdrops, you really only need it to be a little higher than your model is tall (unless you are shooting up at them). But the height of the room will play a factor when you are positioning your lights. For many lighting styles, you want the light to be above the model (looks more natural). So if you have an umbrella or softbox on the light, now you are going to run into trouble when you want to set your light higher than 6 feet. Not to mention that sometimes you might want a light right above your model.
Another factor is the width & length of the space. In most cases, you don't want your model too close to the backdrop. It can cause unwanted shadows and bounce back. Also, you may want/need room between the model & the backdrop so that you can light the backdrop separately. Not to mention that you won't want to be too close to your model. Yet another factor is DOF. If you want to throw your background out of focus, you'll probably need some space there. And if you want to shoot with a black/dark background, you'll have to get the subject as far away from the background as possible.
Going back to the backdrop stand, if they are the light stand type supports, you won't be able to get them right up against the wall, which takes away from your already precious space. If you don't need potable stands, you might consider just using wall brackets and a curtain rod to hang the backdrop closer to the wall.