Not quite there yet, according to this article just posted to the NYT:
Repeal of ‘Don’t Ask, Don’t Tell’ Advances
By a vote of 63 to 33, with six Republicans joining Democrats, the Senate acted to cut off debate on a measure that would let President Obama declare an end to the Clinton-era policy, known as “don’t ask, don’t tell,” which allows gay members of the armed forces to serve only if they keep their sexual orientation a secret. The vote indicated that there was easily enough support to push the measure to final passage.
The Senate must take a second vote to approve the repeal and send it to President Obama for his signature.
I don't yet understand why that is. I'll add updates if it becomes clearer to me.
[Added] In a move low even by their standards, some Republicans in the Senate said yesterday that "the future of an arms treaty with Russia was endangered by Democratic efforts to repeal 'don’t ask don’t tell' at the end of the lame-duck session." Shameless scumbags.
[Added2] TPM is reporting that the second vote is scheduled for 3 pm and this time, it will only take a simple majority to finish the process. I really don't understand the Senate sometimes.
[Added3] CNN says, "Republicans can seek 30 hours of post-cloture debate, but it was not immediately clear whether they would pursue that."
[Added4] C-SPAN's live stream is here, and they're saying on that page that the vote is scheduled for 3 pm (EST). Right now, however, Angry Johnny is yelling about the new START treaty.
[Update 3:30 pm] Okay, they finally did it! DADT IS REPEALED.