On most days it is very hard to get a Ts as a walkup at the MK.During the MVMCP, it is even more difficult because a lot of people want to eat before the party.You can try the Plaza restaurant which is a little easier to walk up to.But I expect CRT,CP, and LTT to be jammed.
I would try to get an ADR, even if you call same day, rather than try to walk in. Don't forget to consider one of the monorail resorts restaurants, especially if you are planning to dine before going to the party. Keep in mind that not all of the MK restaurants are open during MVMCP, so you should plan on dining early.
But if all else fails, I was at Disney for five days last week, on a strict budget, and ate only snacks and counter service meals. You can get by pretty well that way and save yourself some money and time.
Did you try the resorts around MK? I'd be surprised if the GF cafe were booked solid, and we had a nice meal there this past January. My husband had a sandwich that he raved over! It's just a short monorail ride away from MK.