Dan-o,
My buddy and I got ours last year when the leftovers went on sale. I called the Montana FWP to find out the date. For some reason, I'm thinking it was in the summer, June or July, but I could be mistaken. I think they wait until after the June special permit draw as folks who do not draw a special deer permit can return the combo tag and get a refund (80%, I think).
We logged on to the online system when they went on sale and purchased them. I think I woke up at 4 AM to do that, maybe earlier.
Within a few hours, there were no deer combo's left.
There are a lot more Big Game combo licenses available, so you may have some luck with that if the deer combo sells out. Of course, the price is a bit higher...
Good luck!