This is congruent with my observations as well. In my experience, Europeans do see the whole "God bless America" thing as ridiculously nationalistic, the same way many Americans do (cf Parker and Stone's Team America (is that the name?)).
And most Americans see the whole "monarchy" thing as ridiculously anachronistic with kings, queens, dukes, grand dukes, etc. and aristocracy of any kind as having no place in the modern world.
And we Europeans think your big, boxy cars are ugly, so there!