There shall be convened in Santa Fe a committee consisting of the chief justice of the supreme court, as chairman, the speaker of the house of representatives and the minority floor leader of the house of representatives, the president pro tempore of the senate, the minority floor leader of the senate and the state chairmen of those major political parties participating in the presidential primary. The committee shall nominate as presidential primary candidates, and certify to the secretary of state, not later than February 15 before the presidential primary election, the names of all those generally advocated and nationally recognized or supported by any major political party in the state as candidates of the major political parties participating in the presidential primary for the office of president of the United States.