By covering that 10% into fancy algae incubators. It might not be the worst use for a tenth of New Mexico, provided it's the right tenth. I'd definitely nominate Roswell, Artesia and environs, which have no discernible charm to lose by being converted into algae. I'm sure the stuff also smells better than Artesia does currently.
Seriously, though, I assume the chappy in the link was using New Mexico largely just as a land-area comparison. While southwestern states possess certain recommendations for such a project, viz. lots of sunlight and available open space, they have one major negative: there's no water. None. It's all spoken for. One commenter to the linked post asks, "I wonder what portion of the total area of the state of New Mexico is currently dedicated to growing corn for ethanol. 50%? 75%? 100%? More?" Actually, the state's entire harvested cropland represents only about 1.1% of New Mexico's acreage; irrigated cropland about 0.8% (figures from 2002; these numbers are trending significantly downward, I expect because agricultural water rights are being diverted to residential development). These aren't typos, easterners; we are not Iowa. People from other parts of the country really can't imagine how little water we have around here. The video doesn't address whether the water in these algae tanks can be conserved and reused, but if not, that's a deal-breaker in most of the West. Lots of brilliant ideas for using our open spaces and unexplored resources seem not to consider this inconvenient reality.