USA is a democracy as RougeBever said and its political system is difficult for the extremists from the military or other groups to take control in the political parties unless there's a coup or revolution. This is an ASB.
Not really. The best sort of parallel for political party militias is the late period of the Weimar Republic. What is a necessary (though not necessarily sufficient) condition is political, social and economic instability in the state. In essence, the state and the dominant ideology that supports it must be failing.
Reform or the potential for reform needs to be impossible or seen as simply not enough by large sectors of the populace, and further, they need to cling to radical ideological movements instead. Which might lead them to arm, either in self-defense or as part of a conscious plan to begin a putsch against the state.
To get this in the US, the easiest way is to get reform movements after the Great Depression to fail, and for a blundering conservativish government preside over a long, deep economic period of turmoil. Without an FDR like figure to animate the public from 1933 onward towards a reform movement, it's very possible that large portions of the American populace join radical or reactionary movements.
So, conceivably, you could have a mass Communist Party and trade union complex resort to arming themselves to fight against strikebreakers, and reactionary militias.