I think Nixon was pretty savvy; I think he knew the opposition to the war among young Americans was more about the draft than it was concern and solidarity with the people of Southeast Asia (though this was certainly a part of it for the socialist and communist opposition). Once he started to wind down the draft, open opposition to the war diminished.

Arguably the most prominent anti-war song, Fortunate Son, is more about how it’s unfair that the kids of the rich weren’t dying in Vietnam, not that the war itself was immoral.