My guess is that the new coach has already been chosen. Jamie himself has said that he always keeps a short list on all of the coaching positions at ISU. I think Jamie has been having serious discussions with candidates for the last couple of months. It's already a done deal.
I hope JP at least knows of a few guys that would take the job if offered. You can always try to shoot higher, but if you can't lure them in you should at least know of a guy or two that you know will accept the job if offered.
If not, I'm not sure you should make the move to fire Rhoads until you do. Because what if you can't find anyone better?