Motorola promised that Kit Kat would be coming to the Moto X in a "matter of weeks" when they announced the Moto G earlier in the month. The specifics were light at the time, however as we often see with Android updates, the specifics would come down to successful testing and carrier approval. That said, it looks like the AT&T test period has begun.
We have seen several reports of AT&T Moto X users getting invites to test an update through the Motorola Feedback Network. These invite emails haven't specified this is Android 4.4, however given we recently saw Verizon Wireless go through the same process, it would seem strange if this wasn't Kit Kat. As for when this will arrive for all, well, that depends on what happens during the soak test.
In the past these tests have been run over the course of several weeks, or even slightly more than a month. But again we can look towards Verizon who seemed to have ran through the testing period in no time flat. We can hope the same happens for AT&T, but for now, those carrying an AT&T branded Moto X should start keeping an eye out for additional details.
Otherwise, as we learned from the Verizon update, AT&T users will be getting Android 4.4 Kit Kat with highlights to include an improved phone dialer, an improved Gallery, new Hangouts app and more. Some of that more includes enhanced support for NFC Host Card Emulation (HCE), support for the Square credit card reader and Touchless Control support for "Find My Phone."