I think its a bit unfair to call the public 'dumb'. The derision should be squarely aimed at the media and its associated politicians who have created this impression and, it must be said, the academics who have gone along with this 'China is taking over!' narrative. I've said it before on FP.com and I'll say it again: the extent to which the U.S. has declined economically and (therefore) geopolitically should not be underestimated, however taking that serious decline and comparing it to the fact that the U.S. is still overwhelmingly supreme in more or less every economic and geopolitical sense just goes to show how unbalanced the situation was to begin with.
The U.S. has fallen far - but from such great heights that the bottom remains out of sight.
Of course, this is not sensationalistic enough so the narratives of 'beware China!' tend to take over. Hence the misperception.
Blame the lack of intelligent public discourse, not the public per se.