Re: Revolution - season 1 part 2 -
It might be enough to get started, and hope you pick up a groundswell of popular support as you go.
Sure, their army isn't large, but since a VAST majority of the global population is dead, gotta think much smaller. It's not taking over the 250 Million plus of today, it's working on a small fraction of that, spread out over a big distance. No cars/tanks/planes, tv or phones, so you can work smaller areas, campaigns would take years to wrap up.
I could also see a lot of people going over to their side once they heard they were the "real US government". The people rebelling against Monroe wanted to bring back the USA, and as long as the Patriots are able to cover up any negative actions (which would a lot easier in a post-electricity world), and convince people they were telling the truth, I could see a lot of them and other people who remember the US going over to the Patriots.
Over the course of many encounters and many years, I have successfully developed a standard operating procedure for dealing with big, nasty monsters. Run away. Me and Monty Python.
Harry Dresden - Blood Rites (The Dresden Files #6)