I think your chances may be very, very low. Call MS firs thing in the morning to check availability and get yourself on the wait list if there is not availability.
Make certain that at 30 days out, you call and renew your waitlist with MS firs thing in the morning. At the 31 day mark, everyone drops off the waitlist and this may be your best chance of getting a last minute reservation. I got lucky doing this in June for VWL in this manner.
Lots of luck and I'll wish some pixie dust to come your way!