New Mexico State Senator Bill Tallman (D-Albuquerque) has introduced SJR 1, a proposed constitutional amendment that would eliminate the ability of parties to have nominees for congress and state office. Like the similar bills in other states, if enacted, it would make it extremely difficult for minor parties to remain ballot-qualified. They would need to perform very well in the presidential race. Here is the text. It is unclear whether it would permit write-ins in the general election.
Senator Tallman is in his second term and is age 81 years.