Does your library, or senior center or church have big tables? You can probably shove several together.
Ask them if they will let you come on a rainy tuesday morning or sometime when it is not busy, and use the tables to lay out your quilt so you can pin or baste it together. If you can, bring a It is friend or two, and all work on everybodys quilts.
It is amazing how fast it all gets done with helping hands.
Then when you get it home, you will scrunch it up anyway to sew it. So you won't need the space then.
Stay off the floor! When I get down there I am stuck forever! By the way, a big refrigerator cardboard on a bed works wonders for smaller wall quilts and throws - things like that...