N.M. Stat. § 2-3-1
There is created a legislative joint committee of the house and senate to be designated "the New Mexico legislative council," composed of sixteen members, eight from the house and eight from the senate. The president pro tempore and the minority floor leader of the senate and the speaker of the house of representatives and the minority floor leader of the house shall automatically be members of the council. Six of the remaining members shall be appointed from the house of representatives by the speaker; provided that, if the minority is entitled to more than one member, the additional minority members shall be appointed by the speaker only from recommendations made by the minority floor leader, although the speaker shall retain the right to reject any such recommendations; and six of the remaining members shall be appointed from the senate by the committees' committee or, if the appointments are made in the interim, by the president pro tempore after consultation with and agreement of a majority of the members of the committees' committee. If the minority is entitled to more than one member, one of the remaining six members shall be appointed by the senate minority floor leader. The appointed members of the council shall be appointed from each house so as to give the two political parties having the most members in each house the same total proportionate representation on the council as prevails in that house; providing [provided] that in the computation, major fractions shall be counted as whole numbers, and in no event shall either of the two major parties have less than one member from each house. The members shall be appointed for terms of two years or less expiring on the first day of the regular session held in odd-numbered years. The term of any member shall terminate when such member ceases to be a member of the legislature. Provided, however, that members of the council reelected to the legislature shall continue to serve as members of the council until their successors are appointed. Vacancies on the council may be filled for the unexpired term by appointment from the house or senate respectively by the respective appointing authority which makes the original appointments and subject to the same recommendations; provided such new members must be from the same body of the legislature and the same party from which their predecessors were appointed. The council shall elect such other officers as may be deemed necessary from among its own members. The officers shall be elected for terms coterminous with their membership on the council. The speaker and the president pro tempore shall be co-chairmen of the council. No action shall be taken by the council if a majority of the total membership from either house on the council rejects such action. This 1978 amendment shall not be construed to cut short the term of any member already appointed to the council.
NMS § 2-3-1