Lol, The problem is, in the current situation as in the Civil war in 1865, the US Army simply dissolve and forming State Milita otherwise if they keep the US Army as it is, they will not be combat effective as there are bound to be some of the soldier in the same unit do not share the sentiment with the other.
In another word, in case of Civil war, there will not be a United States anymore (the states are not united anymore, hence the civil war) and the United States Army will dissolve and formed into Regional Militia unit. Whatever army you can call them, but they won't be United States Army.......
Eventually if one side win, all the States can be reunited, you can call them United States army again or any other name it seems fit.
I am not even talking about the constitution, How can you fail to see this very clear point