The days that you need to worry most about not being able to enter MK are Christmas Day and New Year’s Eve. And even then, they go through various stages. When the park is approaching capacity, first they’ll close the Transportation and Ticket Center parking lot (the lot for MK). Next they’ll begin to turn away “day trippers”, those guests who have tickets, but are not staying in a Disney hotel (also Swan and Dolphin, Shades of Green, and selected DTD hotels) or have an annual pass. If you are staying at one of those hotels or if you have an annual pass, you will still be able to get in.
However, once they hit full capacity (around 80,000) nobody gets in until enough people leave.
But crowds will be pretty heavy during all of Christmas week.