Just curious ... was the backing indeed too short or was the top mis-matched to the back when loaded on the frame?
I ask because I did this with my first quilt on the long arm. I pieced the back with a 4" "frame" around a center fabric. I remembered to mark the center of the backing at the width side, but not the length side. I discovered this after I loaded the backing (I have zippered leaders), while I was trying to match the position of the top. I didn't want to take the backing off the frame (although with zippers it would have been easy/quick enough - chalk it up to experience) so I tried my best to figure out where the center was. I missed by a few inches. I didn't run out of backing ... but the backing is missing a "frame" at the bottom of the quilt (on the back - so I'm not gonna worry myself!!).