Ask Mr. Smarty Plants

Morella cerifera (Wax myrtle) is a 6-12 foot multi-trunked shrub, but might be considered a tree at its maximum height.   Its distribution, according to the USDA Plants Database, has a western limit at Oklahoma and Texas.   If you will click on Texas on that map you will see that its natural distribution in the state is limited to the eastern third of the state.  You will note that the areas where they occur in the US generally have high rainfall and high humidity. 

In the Growing Conditions section of the species page you will see:

Water Use: High
Light Requirement: Sun , Part Shade
Soil Moisture: Moist , Wet
Soil pH: Acidic (pH<6.8) , Circumneutral (pH 6.8-7.2)
CaCO3 Tolerance: Medium
Drought Tolerance: Medium
Heat Tolerant: yes
Soil Description: Slightly acidic, moist, deep sands, loams, clays.
Conditions Comments: Requires constant moisture to get established, but both drought- and flood-tolerant once established. If temperature goes below zero degrees F, will defoliate, not releafing until spring. Tolerant of saline conditions and urban confinement within pavement.

Here in Austin, in the middle of Texas, where our average rainfall is 33" a year, we are able to grow them as landscape plants; however, this year because of the extreme drought and heat, several of my wax myrtles are dying even though they have received regular irrigation.

I checked the websites of several nurseries that specialize in native plants in your area by entering "New Mexico" in the Search by Location slot in our National Suppliers Directory to see if any of them carried wax myrtles.  My thinking was that if they did, that might indicate that they could survive with special care.  None of the nurseries that I checked carried them.

So, my assessment is that you might be able to get wax myrtles to grow with lots of special care and constant watering, but it will be a struggle and they aren't likely to thrive.  If you go to our New Mexico Recommended page and use the NARROW YOUR SEARCH option to choose "Shrub" under GENERAL APPEARANCE, you will find more than 30 shrubs that are native to New Mexico that will give you much happier results.