My kids watch a lot of tv -- every day starts and ends with a show, and meal times not at school are generally accompanied by a show too. So that's maybe two hours typically, and often more on the weekends. The meal thing is because mommy likes to read while she eats, and doesn't want to talk to them or hear their screechy little voices.
I find the screen thing a little confusing too. Someone was recently talking about a media fast, which sounded well and good until I realized they also included things like listening to music and NPR. And that seems sort of random to me. Why is putting on a record more damaging than reading a book?
Anyway. We'll see what happens as the kids get older. At least so far, it's mostly not been them demanding screen time, but rather us putting it on to keep them semi-occupied as we get shit done. We introduced Anand (age 2 and a bit) to computer games this past week, and that resulted in three days of intensive demands for more games, but again, it's not really about the screen, per se, but rather the new game, I think. And one he can play by himself, without waiting for the attention of an adult.