generally- people use pins when doing it on a floor- visit Alex Anderson's web site, or check the tutorials here- there are a couple u=tube videos too that will show you how to pin your quilt backing to the carpeting for layering/basting.
i would not use duct tape or packing tape- the sticky residue left on the fabrics will be not only unsightly-but difficult to remove.
i also do not have room to lay out a large quilt in my home- i visit the community center- when they do not have anything happening it is not a problem to slide a few tables/chairs out of the way & have a large tiled floor to lay everything out & prepared. and they do not charge for using the space. I've also used a room in the basement of our library also for free.
but check out the tutorials for preparing your quilt for quilting- you will find many useful tips- some people prefer a carpeted floor
(easier on the knees)