The folks at PhoneArena have a tip from a solid insider source suggesting the new Moto X will actually be released around the same time as the Motorola Droid series phones on Verizon. According to their source, the Moto X will hit the streets "somewhat simultaneously" as the new Droid series. Although they weren't more specific than that, a little deductive reasoning suggests we will see the Moto X shipping out somewhere between August 20th and August 23rd. Some unconfirmed previous rumors suggested an August 23rd release date to begin with.
The final official reveal for the Moto X will be on August 1st, so hopefully we will know more specific details at that time. As always we will keep you apprised as more details emerge.