Edit: After half day, my wife’s Mac started having the same problem. I have then applied the solution that I found in the Apple
AT&T Respond To FaceTime Controversy
A lot of hate has been aimed towards AT&T over the previous days after they announced they would only allow the customers using the more expensive Mobile Share plan to use FaceTime over 3G which Apple is introducing in iOS 6
The FCC’s net neutrality rules do not regulate the availability to customers of applications that are preloaded on phones. Indeed, the rules do not require that providers make available any preloaded apps. Rather, they address whether customers are able to download apps that compete with our voice or video telephony services. AT&T does not restrict customers from downloading any such lawful applications, and there are several video chat apps available in the various app stores serving particular operating systems. (I won’t name any of them for fear that I will be accused by these same groups of discriminating in favor of those apps. But just go to your app store on your device and type “video chat.”) Therefore, there is no net neutrality violation.
Basically if FaceTime was a downloadable app from the App store then AT&T would not be able block the service. If this catches on it could migrate over to other platforms such as windows which would would see the same thing happen to Skype and the same with Android and Google Hangouts.