Bornakk confirms that, as Robin posted here the other day, players will need Burning Crusade to complete the Battleground daily quests.
Which brings up the question, yet again, of why there would be people out there who still haven't picked up the expansion that released almost one year ago. It's $30 at Amazon right now (which means you could probably find it in a few places online for less than that), and given all of the content now available, not only in Outland, but back in Azeroth, it's really a no brainer.
Now, maybe you just didn't want to make the investment of the Battlechest, and maybe you haven't yet reached 70 and figure you don't need to play BE or Draenei or do these daily quests. Maybe 60 is good enough for you, and jewelcrafting isn't your thing. But especially with the holidays coming up, it's not surprising at all that Blizzard is placing more and more content behind the Dark Portal. If you haven't installed the expansion yet, why not?