An aggressively stupid person. A true schmoe-donkey combines the hapless, clueless, luckless qualities of a regular schmoe with the stubborn, clumsy qualities of a class-A jackass.
"Who was that random guy at the party?"
"You mean the one drinking all our beer?"
"Yeah, and hitting on all the women, even though they told him to piss off... for like three hours straight."
"Oh, that guy? Yeah, just some schmoe-donkey."