You can't get the new Moto X from any of the carriers directly, but Verizon does have two Motorola devices ready to go right now. The newly announced DROID Maxx 2 and Turbo 2 are on sale through Verizon's website and in stores. The Turbo 2 is the more expensive of the two, but the Maxx 2 isn't what I'd call cheap, either.
The DROID Turbo 2 (below) is a proper 2015 flagship smartphone with a Snapdragon 810 (it is what it is), 3GB of RAM, 32GB of storage, a 5.4-inch 1440p shatter-proof AMOLED display, and a big 3760mAh battery. Verizon says it'll run two days on a charge. The Maxx 2 (above) is based on the Moto X Play outside the US, but it has a Verizon spin. The Maxx 2 has a Snapdragon 615, 2GB of RAM, 16GB of storage, a 5.5-inch 1080p LCD, and a 3630mAh battery (also good for about two days). It doesn't have a shatter-proof display, but it is water-resistant.
Verizon is asking $624 for the Turbo 2, which works out to $26 per month for 24 months. The Maxx 2 is $384 full price, and $16 with monthly payments. Keep in mind that both phones ship with Android 5.1, which is kind of lame. They're supposed to get updates, but well, Verizon. The Turbo 2 will have Moto Maker customization at some point, but that doesn't appear to be live yet.