I just got my FP for Jan 3. Before this, I would get to the booking screen and pick the day and then it would say, 'select another day'. I was checking every day and it just worked today. I don't know how people are getting late January dates.
This is unfortunately a common error. Try logging in using a different email address or create a new email address. We were finally able to get a reservation by using an old email address we had registered with Disney.