On the other hand, I think a larger proportion of people would refuse to believe it purely on partisan lines. So if Biden tried to sell the world on Iraqi WMDs, the Republicans would all refuse to believe it and younger right wingers would call Saddam based for fighting Iran that one time - and if Trump did it then the libs would take the position that he was obviously lying. In neither case would the opinion of the American people affect the actions of the government.
One could easily imagine a situation in which fewer people would reject the lies for good reasons (genuine anti-imperialist analysis, critical assessment of facts, that kind of thing) while at the same time more people would reject the lies for stupid reasons (the claims are all Russian manipulation/made up by the deep state to replace white people).