New Mexico lacks a statute banning same sex marriage. It has always been gender neutral. Only public policy and common law have prevented legal same sex weddings in the state.
... until now
The mayor of Santa Fe and a city councilor will introduce a resolution on March 27 that will advise clerks to start issuing marriage licenses.
The only foreseeable barriers will be opposition on the council or a state court challenge. It is unlikely that one jurisdiction will set statewide policy, likely requiring action from the Democratic attorney general or a ruling from the state supreme court.