They are getting a “connection failed†message. According to the discussion thread on Apple Support Communities, it also doesn’t seem like a carrier related issue, as users are unable to make FaceTime calls either over Wi-Fi or cellular network.
Meanwhile, Apple hasn’t acknowledged the issue yet. Apple’s System Health page is not reporting any outages.
Until now we don’t know if this issue is affecting all iOS 6 users, MacRumors said that one user has mentioned that FaceTime was working on a device running iOS 6.1.6, but did not work on a device running iOS 6.0.1.