Even if someone was able to lie, and get elected, how would they expose? People are not ready to hear the truth about things. No one wants to hear about the violence of the state. Everyone knows about it, but they get pissed when you talk about thinks like voting=violence and cops=bad.
The constitution has nothign to do with your natural right of self defense. It does not matter what is written down on any piece of paper, you always have, and always will enjoy a natural right to self defense, in any situation.