I don't know, I've seen people scrape up entire libraries in a year or two.
Of course doing something like this would pretty much entail that ALL of your money be put towards buying games and pretty much ALL of your time being put towards ebay crawling/garage sailing.
I simply don't think it's impossible. Completely absurd and unlikely, sure.
EDIT: I'm assuming that we're only counting US, licensed, retail console releases, loose, and no variants or anything. I think something like that isn't necessarily impossible.