Absolutely. Also, both of the OTL examples cited by @
Rickshaw (The Gulf of Tonkin and Iraq's alleged WMDs) had one thing in common: They were used as the pretext to escalating/launching a war, something that is much easier to rally popular support via appeals to patriotism. Which is obviously different compared to proposing a peace deal ENDING a war.
... A war that, BTW, from the perspective of the Americans public, they were totally WINNING, and winning massively. In that you had reports in the news for months of these larger than life figures in the form of MacArthur and Patton totally kicking commie butt... Than suddenly the president fired General Patton after he was shot in the line of duty, UN forces pulled back from the Yalu River, and now the Reds are being rewarded with a peace deal that allowed them to walk away with something while we were winning?!
Especially when the lessons of WW2 in the form of
'Compromises with the enemy will never work, since they will just come back for more. Just look at the Munich Agreement and 'Peace in our Time'!' were still fresh on everyone's minds.