That is an issue - the military certainly would be good training ground for an attempted coup. However, while they might have the training, they don't have the equipment, and they really don't have the numbers. So the most likely scenario is they resist some law or refuse some warrant, and get trapped like a Ruby Ridge/Waco event.
Of course it's possible that they would be organized enough, equipped enough, and motivated (i.e. willing for them and their families to die for the cause) enough to start a coup. Anything is possible.
But the FBI/ATF/DEA/US-Marshals can pull in hundreds of agents to respond, ALL will training, and on the right side of the law. 500 federal agents, with military grade hardware, would be a LOT for any well organized group to defeat.
I'm not sure any group has those numbers, organized, with the right equipment.