Having same problem between two iPhones and iMac all logged into Facetime with same Apple ID and worked fine before iOS7. Now I either get "trying to connent" and then cut off or an immediate "not available for FaceTime" message. Seems to depend on which way I'm trying to call.
Have tried:
-variations in phone #s and email addresses
-logging into Facetime on iMac with different Apple ID
-turning Facetime and iMessage on and off
-resetting network settings on iPhone after turning Facetime and iMessage off
-restarting iPhone
-rebooting iPhone
-erasing all content and settings and restoring iPhone from a backup
-forgetting wifi and turning wifi off on both iPhone and iMac, resetting network settings and restaring both
-went thru everything here: http://support.apple.com/kb/ts3367
-several other thing which I can't even remember
The only thing I haven't tried so far is to erase all content and settings from iPhone and setup as new device. Not sure exactly what I would lose and have to set up again. Plus I can't do it to my wife's phone since she's out of town. Hopefully Apple will address the issue in iOS 7.0.3 update very soon.
We also had many other problems ranging from my wife's iMessage not sending messages to our computer suddenly renaming itself saying that the current name was already being used on the network. I was starting to think I created this problem while fixing all those other items but it's starting to sound like this is just another Apple problem.
In case I need to set up as new, can anyone tell me what I would be able to restore from our iMac and what I'd have to put in manually.