When a shitty situation/event/person is forced to be handled and consumed in a social situation.
or a sexual act:
A sexual act consisting of three people, at least one male. While the male is having anal intercourse, he pulls his shitty shaft out, rubs it between the ass cheeks of the anally assaulted partner, while the third person chugs it up.
Much like sucking a dick, however this phrase is much more aggressive. Chugging a dick involves "bouncing" the cock in your throat for a longer amount of time.