"...cartoonist Thomas Nast, about 1862... His cartoons of Boss Tweed were so damaging to the corrupt politician that they were the source for the current word "nasty".

Sorry to spoil a good derivation, pdq, but the word "nasty" has been around for a lot longer than that. Shorter Oxford English Dictionary gives it as "late Middle English, origin unknown", but with the earliest reference being from 1548, with the sense "offensive to smell or taste, nauseous".