Since the FAA/TSA refuses to publish any regulations on this issue, there are no official public documents one way or the other.
Accordingly, whatever the checkpoint goon says, is law that day.
AA allows a small backpack (as opposed to a camping-style pack) and recommends that the personal item be less than 38 linear inches (length + width + height).
www.amrcorp.com/facts/sheets/bagallow.htm
I'd say - check with your airline.