I think the goverment, or rather the goverments, of Mars would be very autonomous and local at first, since the infastructure on Mars will take time to develop and thus the travel times will be slow between individual colonies.
Once it develops we would very well see a Mars Ecumenopolis, or a "planetcity", a city that spans across the entire Martian surface.
This Ecumenopolis would easily be one of the biggest economies in the entire solar system since Mars has the same amount of land mass as Earth does, except the land can be developed efficiently, and planned from the very beginning without wars or other some such straining the efforts to build it.