Any private militia would be ineffective. The armed forces have many types of weapons available to them that would be very effective against such opposition, including drones.
I don't know that the best way for an armed, potentially oppressed population to resist is to organize itself into militias. Like you say, they can be easily infiltrated, and watched.
But with the examples of Iraq, and Afghanistan, and even Vietnam behind us, the power of an armed people against an unwelcome army, even the largest army on the planet, is a real thing.
While it was shown in Iraq to be possible that a powerful army with money to bring key players on board may eventually prevail, Iraq also demonstrates how eternal vigilance is required to maintain power on the basis of a strong army alone.
In the meantime, a steady dribble of body bags flowing into the military cemeteries saps up the confidence and sense of purpose of that army.
Militias are what people who like to play games r form in order to entertain themselves, and appear as macho badasses.
Sleeper cells have demonstrated themselves to be much more under the radar, and ultimately more deadly, and more of a threat.
An armed population with a strong belief in freedom, instilled into them through the very Constitution of the US, would be more formidable an oppenent as anything that the Americans have run into in Iraq, or Afghanistan, or Vietnam.
