"You must have the publics support to wage war."
I had always understood that the American public was still largely supportive of the Vietnam War until the very end.
It was Watergate that lost the Vietnam War. After Nixon got re-elected in 1972, he got our troops out while at the same time ARVN had gotten to the point where it could defeat the NVA (as it did during the Easter Offensive). What happened was that after the 1974 elections in which the Democrats got a veto-proof majority in the House, they then proceeded to stop funding the South Vietnamese. That was all due to Watergate.