Update (January 4): The free packs are here, and can be found in the gift area of Battle.net (the icon is in the upper-right corner, next to your name). The original story from December 21 follows below.
Shortly after the Hearthstone expansion Kobolds & Catacombs went live, Blizzard discovered that the game wasn't behaving exactly as it should. Some players were experiencing delays in receiving new daily quests, because of the load placed on Blizzard's infrastructure by the apparently-unforeseen popularity of Dungeon Runs. It still hasn't been fully fixed, but Blizzard said today that a hotfix has "significantly reduced" wait times, and most players shouldn't notice any extra wait at all.
Those who do encounter a delay may have to wait 10-30 minutes after first logging in before the daily quest appears. You don't need to stay logged in during that time so you can go and do something else while you wait; you might also see things happen a little quicker if you manually refresh the quest log, or play some games in Play Mode or Arena. (No Dungeon Runs, though.) Blizzard said it will continue to work on reducing or eliminating wait times, and hopes to have a proper fix in place after the new year ticks over.
The good news is that to make up for the hassle, Blizzard is giving everyone three free Kobolds & Catacombs card packs. The packs will arrive as a Battle.net gift in early January.