More can be said but you might want to check out this answer I wrote.

In effect - US public opinion on the Vietnam War was always known and monitored by polling groups like Gallup. Indeed , the Johnson Administration had a heightened fear of negative public opinion and shaped much of its war strategy and policies in the hopes of avoiding this reaction. Some important takeaways are that public support for US involvement in the war started at around 60% in favor and 24% against in 1965, and steadily fell to 60% against and 29% in favor in 1973, with the majority turning point happening at August 1968.

This isn't the same as public support for LBJ's handling of the war, and this support dropped off much more quickly before stabilizing around the high 40s in 1967. However however, even that opposition needs to be parsed - quite a few respondents thought that LBJ was putting too many restrictions on the prosecution of the war, and neither opposition to LBJ nor opposition to the war in general necessarily meant support for the antiwar movement.