It all depends on how long you're willing to spend on the site.
People with 2000 games don't play all their moves on the same day- with 3 day time limits, they can get away with about 700 moves a day. But if you don't have the time to come online and play 700 moves, then obviously you would be overwhelmed by this many games.
How many games does it take to be overwhelmed. I saw a person with over 2000 and unlike other people they don't take vacations to manage the games. Any thoughts?