Who agrees that once a PM lies, they should be stripped of the position?

I believe so. Julia Gillard flat out lied, there is no way around it. If she had said something like "There will probably not be a carbon tax", then that's different. However, she said "There will be no carbon tax". She needs to go. I am not biased, I would say the same about any PM. John Howard lying about GST is not the same, as he changed his mind before the election that he won, and subsequently implemented it.