Like some have said, it can be done, but be prepared with an alternate plan or a long wait. I think that if you show up very early (or late in the morning) you may have a better shot.
In the past we've shown up early and gotten in with no reservations, and have made reservations the same day for dinner.
Seems like this whole internet thing and Dining plans are really making it harder to get in... Years ago, it used to be you could walk up early and get in (and the other character meals as well). Now with everyone making reservations (and not showing up) and having dining plans it's harder to get in!
Also - many times you call up for a reservation, and they say "we only have time x". Ok, you take it, and when you get there, half the restaurant is empty. I've also been turned away from restaurants "no space, sorry", called up and gotten a reservation for 15 minutes later (back to the podium we go!).
So... it's all a crap shoot.
Jose