My very first quilt was backed with, and some piecing done with, a sheet. But, since it was my first, it was polyester. I did not know the difference way back then. Needless to say, the sheet has held out better than the inexpensive cottons (anyone remember House Of Fabrics?). The only problem I had with the polyester, was that it would pucker a bit if sewn on the straight of grain. I don't typically use sheets nowadays, as most of my quilts are art quilts, and usually entered into a show. So I use the good/expensive stuff. But, if I am making a baby quilt or a quilt for charity, a cotton sheet works just fine!
Dawn