There was a scene in the books after the death of TR where Flora is talking with some of the other Socialists leaders, and she notes that if TR had called out the troops so he could stay in power after losing the 1920 election they might have answered that call. Thus the idea of a military coup wasn't unthinkable in the TL-191 United States.
the argument surely cannot be "Flora's views about X are in the text, and therefore plausible," because she is the one who discusses Canadian statehood. Perhaps the times have changed? But umm, then surely the chances of an army coup have too?