The Moto X is available with a wide variety of US carriers at this point, however your ability to tinker with the phone will vary depending on which carrier you have. Motorola does offer an option to unlock the bootloader, however that option is not available for those with AT&T and Verizon Wireless. But official paths aside, it looks like someone has managed to get past some of the blocks and has achieved root access on the Verizon Moto X.
That someone is well known in the Android world and can be found as @TeamAndIRC, aka Justin Case on Twitter. Anyway, the achievement was noted with a simple message that read as follows; "Just rooted @davekover's Verizon MotoX." While this is likely good news for those who are looking to play around with a Verizon Moto X -- there isn't any need to celebrate just yet.
Basically, while he has achieved root access, he has yet to release details of how. Or in other words, the Verizon Moto X can be rooted, but not by anyone and everyone just yet. Further tweets also make it clear that if you have a Verizon Moto X and are planning/hoping to be able to root it soon -- you should not accept any updates while you are waiting.
Otherwise, at the present time there still appears more work to be done as there was also mention of how this was root shell, but done without having su installed. Simply put, this was more of a temporary root. But in the end, it does appear as if progress is being made and that Verizon Moto X users will be able to have root access should they desire it.