It ain't an original. I'm sixty-five and grew up less than thirty miles from Tama, Iowa; which is the home of the Meskwaki Nation. It is not a "reservation", as the injuns that were run off of it and run off to Oklahoma, worked diligently and saved ... in order to come back and buy their own ancestral land. Neat folks.
But, they did like their liquor. So, on payday ... you stayed away from tribal lands ... and the townie bars that they frequented. They raised some ruckus, to put it mildly. So, "Drunker 'n three injuns on payday" was simply an observation that worked its way into a colloquialism.
Truth is stranger than fiction.