I'd characterize the typical U.S. leftist as not really having the foggiest clue about Marx beyond his having some vaguely important relationship to Soviet-style communism, and as not having a clear stance regarding communism or capitalism... either because they actively support a mixed economy, or because they are confused about economics.

I think this is true, but with the caveat that a lot of the memes circulating among educated leftists in the US are basically Marxian in their approach to class and economics. Usually not orthodox Marxist, though, and they fall well short of cohering into a complete Marxian analysis anywhere outside of sociology departments and the odd punk show.

Joe Left is generally not aware of this. Joe Right probably has a confused idea of the relation ("communist" is a dirty word in the US, so right-wing news outlets don't miss opportunities to use it), but is unaware of the Marxian/Marxist distinction and thinks it makes Joe Left an outright commie.