I'm not sure what the Constitution has to do with Viet Nam.
Before you put on the green suit. You take an oath to defend the constitution. AND to follow the orders of the commander and chief. Where he says go,you go. If you are a U.S. Solider, you have to have faith in the People to not put a nitwit in the White house. Remember, many of the guys were drafted. They took the oath. And they lived up to it. Despite how they might have felt about that particular war.
Back when chicken toejam was the prez, I saw an interview show on TV. It had a few military officers on. They were explaining that the reason they resigned their commission. Was because clinton was the commander and chief. While my sympathies were with them. My respect went to the guys that stayed in uniform, and continued to guard this country. Regardless of who was in office.
..." Article II, Section 2 states that "the President shall be commander-in-chief of the army and navy of the United States; and of the militia of the several states, when called into the actual service of the United States..."