It’s not physics, so one has to put together a circumstantial case. I’ve written about the way it looks to me.
In brief, the war was always unpopular, even when Kennedy launched it in 1962. That’s why he hoped that US forces could withdraw — AFTER victory, as he continually and forcefully emphasized, to the day of the assassination. Unpopularity turned to serious opposition to the war by about 1967. It was sufficient to prevent the government from declaring a national emergency, which would probably have been good for the economy, as it was during WW II. Instead, they had to fight a “guns-and-butter” war — to buy off the population to quell dissent.
That’s definitely bad for the economy, and combined with other world events, was leading to stagflation. The Tet offensive in Jan 1968 convinced business elites that the costs were mounting too high — and the more sophisticated understood that the major war aims had already been achieved anyway. By then opposition was so strong that the Joint Chiefs were unwilling to send more troops because they were concerned that they might need them for civil disorder control in the US. LBJ was effectively instructed to move towards “Vietnamization,” troop withdrawal, shifting of the (very visible) bombing of the North to bombing of Laos (easier to keep “invisible”), negotiations, etc., and not to run for re-election. And it suddenly turned out that intellectuals and political figures had always been (secret) “long-time opponents of the war”: their strong support for the war was sent down the memory hole. One of the most interesting features — but unmentionable, though well documented — is the radical rewriting of memoirs of the Kennedy administration to “prove” that he was really a dove all along, and “memories” about the early opposition of elites (particularly JFK) to the war, refuted by overwhelming evidence at the time, but taken seriously.
The anti-war movement played a crucial role, by creating circumstances under which elites turned against further escalation, and limits were placed on the extent of destruction possible — leaving a monstrous horror story, but it could have been a lot worse.
…The uproar set up conditions in which business and intellectual elites became tepid opponents of the war, never on principled grounds.
The public, in contrast, opposed the war as “fundamentally wrong and immoral,” not “a mistake”; about 70% by 1969.