Hi. I have a 2012 CTS and and iPhone 5. I had the same issue until a few minutes ago. Since I got the iPhone 5, my CTS acted like its bluetooth was disabled. My new iPhone 5 kept "searching" and never would acknowledge the Bluetooth connection in my car (as if it was indeed turned off or disabled).
I wasn't aware of diesel vdub's post until after figuring out the issue myself. However, he is correct.
(Check your owner's manual for detailed instructions.) I had to delete my old iPhone 4's pairing through my CTS's Handsfree system then pair my car with the new iPhone 5. Once I deleted the old iPhone, my new iPhone 5 started picking up the Bluetooth connection in my CTS. It only takes a few seconds to do. I'm SO happy! I've been fretting over the issue since I got my iPhone 5 a couple weeks ago. Up to this point, I thought that the issue was with the iOS 6. Apparently, it isn't.