I have used the "future daycare" for two separate sets of Pokemon and both of them were able to produce eggs without issues. Try removing the parents from the daycare and placing them back into the daycare to reset it. Also, your account needs to be online for the game time to count toward the daycare egg production.
Sometimes it can take as long as 9 hours to receive an egg from parents of different species. If you've only been online 2-3 hours a day, it's not too far fetched to say you just hadn't been online long enough.