I got approved! And in only 4 days after fingerprint receipt, which was a welcome surprise.
It seems that for some people it takes a few days and for others it takes a few weeks. I'm not sure why, but I have a feeling those who have already gone through this process before (I went through it with the DOJ in July) aren't waiting as long.
A colleague of mine received the "fingerprints received" e-mail 4 days before me, and has yet to receive approval (this is her first background check).