I store my larger cutting mat under my bed. That might work for you? You might also find June Taylor's Shape Cut ruler handy? I couldn't cut out a quilt without it. Read the instructions carefully if you decide to get one and if you do't have another quilter to show you how to use it... but it is my favorite ruler. I got mine at Wal-Mart, though I know that Hancick's and Hobby Lobby both have them, or at least they do here.
Who says you have to cut the pieces out perfectly anyway...
Dina