But seriously, modernity itself is influenced by Marx. Profoundly. (It's also influenced by, for example, Newton, Voltaire, Comte.) If any more profoundly in the case of the Democratic Party than in other cases, only by a trivial amount, relatively speaking.
Basically this was going to be my attempt at a 'serious' answer. I would say though the ghost of vulgar marxism consistently haunts all political discourse to this even in places where at first glance Marx is the 'enemy' (American conservatism are fond of what might be termed 'reserve vulgar marxism' in their rhetoric for example).
Nice, but you should've said the "spectre of vulgar Marxism" rather than the ghost.