To screw up really badly. To miss the point of something and do something else. Comes from the idea that when having sex, one misses the pussy and starts humping a woman's gooch, the area between her pussy and ass, making a fool out of himself and screwing up. Don Eimus is a person screwed the gooch when he disrespected some thugish black-woman basketball players.
"I knew I should't have nailed Monica Lewinski... Damn i screwed the gooch."
I did my report completely wrong. Man i really screwed the gooch."
"Matt, youre' a jew so don't have sex with that terrorist's daughter. You'd have to be a total dumbass to screw the gooch like that"