Eucalyptus trees can grow to be very large trees if given the right climate, however in Southern New Mexico, the tree usually dies back to ground level and comes back up in the spring as a shrub.
The Eucalyptus tree is not really recommended for the Southwest, but if you want to try a small ornamental variety in a well protected patio area, you may be OK.
If you can containerize it, and bring it indoors if freezing temps are in the forecast that would be even better.