New Mexico does not issue Marriage Licenses to same-sex-couples. It is also unclear whether the current State Laws honor same-sex marriages performed in other jurisdictions. 

"While we cannot predict how a New Mexico court would rule on this issue, after review of the law in this area, it is our opinion that a same-sex marriage that is valid under the laws of the country or state where it was consummated would likewise be found valid in New Mexico." -Gary K. King Attorney General

Sources: Lambda Legal and NMAG