Here's a handy little document I just noticed on the Legislature's website. It tells you, year by year since statehood, which party has ruled the state House of Representatives and state Senate.
It's a pretty good history lesson. Here's some factoids that stand out.
* The Democrats have controlled the state House since 1929, except the 1953-54 session.
* There were two years in the '80s when Republicans actually had a 22-20 majority in the Senate.
Otherwise, Democrats have controlled the Senate every year since 1933.
* Republicans controlled the Senate every year from 1912 (the first year of statehood) until 1933.
* The GOP controlled the House every year from 1912 through 1923. Power see-sawed between the parties during the Roaring '20s..
* With the exception of Independent Andy Nunez in 2011, there have not been members of any party except Democrats and Republicans since 1916. According to Tracey Kimball of the Legislative Council Service, there were five New Mexico lawmakers who were "progressive Republicans," aka Bull Moose Party members between 1912 and 1916. And there was one real live socialist elected to the House during the early years. W. C. Tharp House served in the 1915 and 1916. He represented a district in Curry County, which, at least in recent years, is not considered a hotbed of socialism.
Have a look at the chart: (Enlarge for the sake of your eyeballs)
Correction 4:56 p.m.: Andy Nunez is an independent, not "interdependent" as I had in the first version of this. That's been corrected in the text. (Thanks, Tom.)
UPDATE: 6:25 pm As promised, I updated info on third-party members in the Legislature and also corrected hte text to reflect the fact that Republicans actually controlled the House in 1953. (Thanks Fred)