One would have to take into consideration the many variables of a zombie infestation, first off the very source of the infection, it could be viral, mystical or other. From the biological viewpoint, a virus can be spread through contact, but must incubate for a somewhat set amount of time, it could rapidly reproduce, but no real virus can at a rate we see in a typical movie, so under 'normal' circumstances a widespread zombie outbreak would be unlikely. As a mystical/magic outbreak could be far more quicker, imagine all the dead of the earth rising simultaneously through some ritual or the wrath of God? It's still as unlikely as a viral outbreak. On the 'other' side we have things like cosmic radiation, mutation and organic modification, more fiction than hard science fact, but are all as likely as the other two sources.
My money is on parasitic infection, Toxoplasmosis, a parasite that over half of the worlds population has already (if you've changed cat litter before, you probably have it already) , it causes zombie like activity in infected rats, including all the zombie traits, except undeath. If it could ever mutate to actually infect humans (we do carry it), it could turn half the population of our planet into zombie like things.
The military and government would be disabled rather quickly in any event, as they too would take losses to the infection just like anyone else, and more so, as the would act as first responders to such a threat.
I wont even start to complain about the logic behind 'fast zombies'