Term used to describe someone who is trying to be overly responsible, or someone who gets drunk and acts responsible. Also used for someone who isn't responsible but who tries to impose the image of being responsible.
"Dude Chris is being McResponsible agian, what a douche!"
"I can take care of myself, stop being such a McResponsible asshole"
" Don't worry guys go be drunk idiots, I'll stay here and make sure everything is OK I'll be McResponsible"