Depending on the games and how much thought I put into picking them...
I could probably do a couple weeks no problem. Maybe stretch it out to a month if i do really well picking.
If I had my full game collection I could probably do a few months and really chew into the backlog. I would definitely be starting to get lonely by that point though so that's probably the limit with no internet.
If I had internet and could communicate with others through it, it probably becomes a good bit longer.