I changed the DNS on my Mac to 8.8.8.8. Wouldn't update the iPhone or iPad either via iTunes through the computer, or OTA. Changed the DNS on the iPad and was able to update OTA. (The irony is that I don't really care about updating the iPad, because it's going away on Friday when the new one arrives.)
Changed the DNS on the iPhone, no joy. I've tried at least five times, both OTA and connected to the computer. I spoke to Apple, and the CSR told me that I had to be patient. I have trouble believing that the servers are still getting slammed, but that's what I was told. So I guess I'm just giving up.