Where did the stereotypical Native American " me tellum..." accent come from?

by 16tonweight

The one that's used in... let's say antiquated jokes like this one (warning, NSFW).

The accent involves a simplified grammatical structure, with the affix <um> added at the end of most verbs. The affix seems like too specific a feature to just come from thin air, or a general sense of "bad" English, so where did it originate?

JohnnyEnzyme

If I could add on-- what's the origin of pidgin expressions like "pale face," "big chief," "how" and "ugh," commonly used in 20th-century literature and in Hollywood?

I would guess there's a strong relationship to OP's question; is that true?