The current designation for such activities in use at most of the staff officer training courses I've attended or of which I'm aware is no longer martial law, but is nowadays referred to as Military Rule.
I was wondering though, does "martial law" not include local and state police, or, as your definition suggests, is it strictly military? The classic definition, of course, only brings the military to bear when the civilian population or other circumstances have exceeded the normal civil authority.
Given Obama's distaste for all things military, I should think that his preferred brand of "martial law" would be the burgeoning DHS. Watching their rapid growth makes it all the more unnerving to witness the humiliation of local and state police that he seems to be slowly wrapping around his little finger.
I am somewhat troubled at how all the pieces will be fitting together. The rapid influx of criminals across the southern border, the arming of the DHS, increasing military urban exercises, the emasculation of traditional law enforcement, the role of muslims in the black community's problems, islamo-sleeper cells, and an executive branch intent on stirring this stew to the boiling point.
Should make for an interesting debut to the next election.