Yes, he did. I think it was at least partially a function of the entire media turning nasty around him. I can't imagine his old boss Johnny Carson cracking filthy jokes about Bristol Palin on his show, for example.
Actually, if I recall, the nasty “joke” was about 13 year old Willow Palin being molested by Yankees player Alex Rodriguez. And even had it been intended for Bristol, it was still disgusting. But by saying Willow, it was the lower than slime in the sewer, and so is he.
Letterman should have been fired on the spot.