They do take walk-ins, but when we went in mid-Sept. (the "lower" season compared to summer or the holidays), the place was PACKED and I was so relieved we had made a reservation. I didn't make it at exactly 60 days out, probably closer to a month out as I was wavering on whether it was worth taking the time off to do that instead of riding something or seeing a show that the whole family could enjoy.
I didn't get my ideal time, as I had wanted to do it before lunch at Ariel's Grotto, but it was good enough. Note that a Photopass Photographer told me that it is sometimes REALLY dead in there in the afternoon (to the point where she mentioned trying to stay awake and nodding off/jerking awake again!). So if you don't care about timing and can do it in the afternoon, that is your best bet for a walk-in and doesn't commit you to "wasting" precious time watching one member of the family get dolled up.