Same thing happened to my i5 I got launch day. Only the far left side of the phone would work. I was on 6.1.2 and jailbroken, so I just used an activator tweak to lock my screen. A friend swapped his phone at apple and got a 6.1.2 replacement, so I took my chances and took mine in. I got a 6.1.2 refurb. I have applecare + but since it was a standard warranty issue, it was a no charge replacement and applecare wasnt even needed. I asked, and my apple care + would carry onto the new device. If you have this issue and still want 6.1.2, I suggest going as quickly as possible for the best chance of getting a 6.1.2 refurb.
Note: you do not get a "new" phone. My friend kept saying new in box, but it was a refurb phone that came in a blank white box. No extra cables or another headset, just a refurb "new" one. I was happy with the refurb, since the apple lady said they replace the screen and battery for all refurbs. I have noticed a great improvement in battery life. My work is littered with deadspots, and is constantly searching for signal which drains the battery.