Yes, of course you can quilt a big quilt on most regular sewing machines. It can get bulky and cumbersome, but it CAN be done. I do it all the time.
You can even break them down and do them in units - in panels or in blocks (like Georgia Bonesteel's Lap Quilting). There are probably books at your public library that can help you get started with that.
If time really isn't an object, you could even hand quilt them! :D