Martial law and all that comes with it have been predicted by political opponents of every president as long as I can remember and obviously, has never come about (except for the Civil War or non-political, small scale, temporary, cases like natural disasters).
The fact of the matter is, martial law is messy and would shut off many of the luxuries that those who could declare it rely on. It wouldn't be declared unless the alternative is worse.
These leaders like to be able to drive around in peace, hob nob with celebrities, have glitzy parties, drive expensive vehicles, and have servants wait on their every need. Doomsayer predictions of martial law would turn all that upside down. It is messy, would require sacrifice and work on their part, and would mean a degradation in the lifestyle they have.
No, it is too messy. Plus, with modern technology and modern media, you don't need to do something like martial law. You can simply plant stories to people and control their actions much easier. The word is far more powerful in many cases, than the gun.