I walked my endorsement application in on Monday and it was put in the mail the same afternoon. I got it on Wednesday. If you have no arrests disclosed on your application it is possible to get it the same day.
It doesn't take long at all. I graduated on December 10th (although I don't know what date my school sent my papers off) and had my temp shortly after Christmas, maybe a day or two before. I was out of town that week and didn't check the mail until after the holidays. As soon as it is issued by the board, your temp license/permit can be verified via the lsbn website. I was able to verify mine online on December 22.