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Yes, there is an oath that attorneys must take when they are sworn into the bar. It is different in every State.
I was unable to locate the exact wording of the oath in New Mexico, there may not be any official wording. But you can see in this link from the New Mexico State Bar Association, that attorneys do take an oath ... " to uphold the law and abide by the Rules of Professional Conduct promulgated by the Supreme Court of New Mexico." That may be all there is to it. See the language here: http://www.nmbar.org/public/publicpubs/complaints.html
When attorneys are sworn in, a Supreme Court Justice usually administers the oath. In this case, it is probably the word choice of that particular justice, but the idea is the same- uphold the Constitution and Ethics Code.
Here is copy of the New Mexico Ethic Code for attorneys, called the Rules of Professional Conduct: http://www.law.cornell.edu/ethics/nm/code/NM_CODE.htm