It's not a potassium pill, that would be pointless. It's Potassium Iodide. The crucial point here is the Iodine - The thyroid gland (which is in your neck) will readily take up any Iodine, including radioactive Iodine. In the event of a nuclear exposure the thyroid gland would accumulate irradiated Iodine and thus act a repository for it, increasing your effective dose.
By taking the KI pills you fill your thyroid gland up with non irradiated Iodine, meaning that there is no room for any other type.
To be honest, nothing can protect you from a hefty dose of gamma radiation (except perhaps a lead suit) but having a non-irradiated thyroid will prevent continued exposure and, dare I say it, administering these pills makes the public feel safer that the administration is 'doing something'
So, all this talk of K+ / Na+ balance Shiato - all very interesting and gives you an excuse to talk physiology, but kinda misses the point.
Google 'potassium iodide' for more info
Hope that's cleared up a few things.
linkypoos:
http://www.bt.cdc.gov/radiation/ki.asp