not a good idea :( :(
Using a bed sheet for the backing for a quilt is only good for utility blanket quilts. The weave of the sheet is different than the weave of yardage. Why waste all the time piecing a quilt top and then use the wrong type fabric for the backing that is too thick and too tightly woven.
Read info on this site
http://www.reddawn.net/quilt/backings.htm