Same problem here with a new iPhone6. When I tried to set up TouchID, I got a message that it Failed, try again, just like in this 6-second video:
http://www.youtube.com/watch?v=f620pz-Dyk0
The solution is to return it for replacement or refund.
It is an uncommon problem that was unfamiliar to the tech support guy at AT&T, with whom I spent 20 minutes on the phone. He wanted me to do all kinds of time-wasting stuff like hook up the phone to a computer and follow his instructions.
If you bought it from AT&T, do not make the mistake of calling customer service and telling them that you received a defective phone. They will waste immense amounts of your time and refuse to replace the phone; instead they try to weasel out of their 14-day remorse-period obligation to refund your money by pretending that this is a warranty-replacement issue that is Apple's problem, and they will transfer you to Apple, who will only be able to send you a reconditioned or repaired phone as a replacement under the warranty. So don't mention the word "defective" when you talk to AT&T. Instead, if you tell AT&T customer service that you just don't like the phone and you want a refund, they will serve you quickly.