It is not likely that they will take walk-ins as this has become such a popular character breakfast. I would give it a try though. You could also try calling every day until your trip. There are some alternatives if you can't get into Chef Mickey's. If seeing Mickey is a must, you could try 'Ohana's at the Poly, Garden Grill at Epcot or Donald's Breakfastosaurus at AK. My personal favorite is Cape May Cafe at the BC (no Mickey here). Other character meals we enjoy are Crystal Palace in MK (Pooh & Friends) and 1900 Park Fair at the GF (has a variety of characters).
Good luck!
(Just noticed I am now a DIS Veteran!) WOO HOO!