Sure. But killing him doesn't do anything -- except perhaps satisfy a need for revenge -- that isn't accomplished by life imprisonment. And considering that innocent people are almost certainly put to death by the state, one has to wonder what is the acceptable ratio. One "oops!" for every hundred instances of revenge? Two? Ten?
On a slightly unrelated note, I am always surprised when conservatives -- ostensibly supporters of small government -- are usually the ones pushing the hardest for granting the state one of the highest powers imaginable. Just another strange bedfellow, suppose.