Assuming that the police have no restriction in the use of force, it would be very simple for them to pacify a rather large area with an APC and Police. All they have to do is kill a few people who are out of line, and the rest will cower.
No single or small group of citizens in the US really has the ability to stand up to even a single measly APC. The firepower required to stop one is beyond what anybody outside the US enforcement structure can realistically obtain. You may be able to limit its movement with well constructed roadblocks, but harming the vehicle or its passengers with an assortment of shotguns, handguns and IEDs is not reasonable to expect (given they were explicitly designed to withstand these threats).