The police will have a hard time dealing with any large-scale armed insurgency, even if all the insurgents have is small arms. They simply don't have the number

The police will have a hard time dealing with any large-scale armed insurgency, even if all the insurgents have is small arms. They simply don't have the numbers. In US in particular, this is further exacerbated by the kind of weaponry that civilians have access to. For example, a .50 BMG anti-materiel rifle is perfectly legal to own in most states. So is HEIAP ammunition for it. This combination can, with some skill, take down (unarmored) helicopters. And yes, there are people who have this kind of stuff. As far as the military, when discussing these scenarios, keep in mind that their choices, in addition to "support the president" and "oppose the president" include "do nothing". I wouldn't be surprised if that is exactly what's going to happen in the even of a full-fledged constitutional crisis escalating into paramilitary violence.