New Mexico Constitution Art. V, § 7. Succession to office of governor

If at the time fixed for the beginning of the term of the governor, the governor-elect shall have died, the lieutenant governor-elect shall become governor. If a governor shall not have been chosen before the time fixed for the beginning of his term, or if the governor-elect shall have failed to qualify, then the lieutenant governor-elect shall act as governor until a governor shall have qualified; and the legislature may by law provide for the case wherein neither a governor-elect nor a lieutenant governor-elect shall have qualified, declaring who shall then act as governor, or the manner in which one who is to act shall be selected, and such person shall act accordingly until a governor or lieutenant governor shall have qualified.

If after the governor-elect has qualified a vacancy occurs in the office of governor, the lieutenant governor shall succeed to that office, and to all the powers, duties and emoluments thereof, provided he has by that time qualified for the office of lieutenant governor. In case the governor is absent from the state, or is for any reason unable to perform his duties, the lieutenant governor shall act as governor, with all the powers, duties and emoluments of that office until such disability be removed. In case there is no lieutenant governor, or in case he is for any reason unable to perform the duties of governor, then the secretary of state shall perform the duties of governor, and, in case there is no secretary of state, then the president pro tempore of the senate, or in case there is no president pro tempore of the senate, or he is for any reason unable to perform the duties of governor, then the speaker of the house shall succeed to the office of governor, or act as governor as hereinbefore provided.