Our "governing authority" is for all practical purposes the Constitution, and not some living, breathing, human authority like a king or governor. It is not possible for someone to be in a state of "rebellion" while faithfully supporting and defending the constitution, even if this means that someone is at odds with one official or all of them. You see, it is often as not the "authority" or government official who is in rebellion... against the constitution. Opposing such officials does not a rebellion make, though being a constitutional republic there are procedures to be followed before going "last resort."
What if this government was installed by fraud?