Well if you hit it at the wrong time, i.e. a return date after a major holiday and at the wrongtime, it can be a pretty long wait. The highest I've seen was a 20 min wait posted, and I don't even think it took 20 mins. I guess it just really depends on what happens after you get your id...
I would wait a few weeks/month since you said you weren't doing alot of travel till the end of '05. My parents went to get the ID stuff done and after you give them your eye and thumb then they do some kind of crazy background check on you before they issue you your card. *edit* No clue how...
Just to clear some stuff up on the program. You still have to go thru the metal detectors. The only thing that the program allows you to skip is the area where the security guards are checking ids to plane tickets. So instead of getting out your ID you'll just stick your thumb or eye and viola.
*EDIT* Nevermind ignore this answer as you already said that it is not in Liberty Square
I'm not sure of the correct name but is this from "Sleepy Hollow" That eating place that is right between The Hall of Presidents show/store and the walkway to the castle.