If radiation destroys red blood cells in very short order

If as Colonel Donahue says radiation destroys red blood cells in very short order, why does the military even need their experimental gas to deal with the vampires? Surely, eventually, the red blood cells supply will be in too short order and the vampires will die off. The problem should eventually take care of itself. Most everyone will probably be dead by then, but that's not the military's problem. :)