For me, Touch ID doesn't work when plugged in...it does work when not plugged in. (this is a new iPhone out of the box yesterday). Im plugged in to a standard lightning cable and into USB on my Mac.
>>>>> [Try removing the case from the phone, and hold the iPhone in your hand, ...and make sure you are using a new USB lightning cable plugged in to an apple device or the original apple converter (square block plug)]
For me, unplugged: touch ID works every time; plugging it in, touch ID works intermittently maybe 1 of 20 trys. Its like it doesn't see the presence of a finger.
I reset all my finger prints -no improvement.
I called Apple care. During my call with Apple-care, one of the first 5 questions they asked me was "does this problem occur when plugged-in or not" --(obviously they know of some issue). ...... they made me hard-reset and also Erase all data and reload. After reload of my data, still have the problem... in fact it could not perform the Touch ID Setup activity while plugged in.
I tried multiple lightning cables. Reset again as a "new phone"... the touch ID was still intermittently not working during the Touch ID Setup.
I finally removed my case (silicone apple case) ... It turns out that possibly there is an electrical grounding problem with iPhone 6. When my hand is touching the back metal case of the phone, the touch ID works even when plugged in. If I am not touching the metal case on the back, touch ID has problems when plugged in.