Remove the part where it's easy to get things Stateside, and I assure you, a U.S. military coup/junta will be fighting a two sided war as well. Both internal from the populace, and external from former Allies who in no way, shape, or form are going to sit idly by and be threatened by a militaristic U.S. Armed Forces that's even remotely controversial enough to even be considered a coup by the populace.
People forget: The Army Sabotage Manual is public domain.
The military knows exactly the hell it will be entrenched in if it ever goes against the public's wishes. They literally wrote the book.