We have booked a cruise 8 days before sailing and only one brunch day (Nassau, Dream) and were able to get a reservation.
Like PP said, find where and what time to be where they make Palo reservations in your Navigator when you get to port.
Get there 30 minutes or so prior and may be able to get one. We were #2 in line and got a brunch. The crazy thing was during our brunch, there were many open tables, I was surprised.
Good Luck!