The first present I ever remember getting was a quilt from my Grandma. Double-knit polyester patchwork, hand knotted and backed with a sheet. I loved the pattern of the sheet, but it had worn out by the time I was in high school (so, maybe 15 years). My sister got one backed with yardage, and it was still going strong. I'm hesitant to use sheets because of this experience; I don't know why that one wore so badly, but it was heartbreaking.
That being said, if you can get a low thread count cotton sheet made from good quality cotton, I imagine it would be ok. My mom was in a charity group that used sheets as backing, and it worked well enough, although it was hard to find suitable sheets.