I never carry my passport after having it stolen from my in-laws house in Carilo (we later found it discarded on the side of the road).
When I make purchases with plastic, I show them my New York State driver's license, now expired, but it always works.
I sort of assumed it would be a police check like you get on long distance buses. Which you should really have your passport for, just in case they get snotty. Not like you can pop home and get it if you're half way across the country.
I might be completely wrong here but as far as I was aware, tourists have to have their passports with them to book/travel on a long distance bus trip within Argentina (I did going from Baires to iguazu - Arg side)...but for the bus company, not for a police check. I don't know whether they'd check your visa or not if you weren't going to be crossing a border...or care if it were expired. Check with the bus company.
If I were you, I would avoid carrying a passport at all costs, especially if its not valid. I've never seen seen a policeman ask anyone for their passports randomly.