Cobra II is a major work. It is in this that it is made eminently clear that it is Rummy who was in charge of troop numbers. He pressured the generals, particularly Franks, to reduce the numbers over and over and over again until the General(s), knowing what was good for him/them, acceded.
The war itself was fraught with miscommunications, incompatibilities and wildly inaccurate assumptions. In one instance several Air Force bombers were unable to make it all the way back home from their mission because their refueling connections were incompatible with the system in use on the Navy tanker planes. Many more such FUBAR moments are portrayed here.