Hearing this line spoken in earnest is a clear indication you're probably dealing with a yuppie or hipster douchebag, as anybody who's actually a "big deal" lets their actions speak for themselves and doesn't need to mention it to strangers, even jokingly.
Since the original meaning has now been clearly identified as being douchey in the extreme, many people now use the phrase as a witty, ironic form of self-deprecation. The line between the two remains very grey and contextual, however; just because somebody's aiming for a humorous reaction doesn't mean they're not actually serious.
"Oh, not much. I just do corporate law for Fnortner and Finch...gave me a corner office and a Jaguar last year. Got to meet Jude Law last week. Eh, I'm kind of a big deal over there, you know?"
"Oh wow! You're such a cool and humble dude!"
"Yeah, I know, right?"