"I wonder if Tom Apodaca is any kin to former NM Governor Jerry Apodaca?"
It would be a longshot. Governor Jerry Apodaca was born in Las Cruces, NM in 1934, probably a descendant of the Spaniards who settled New Mexico centuries ago (Apodaca is an old Spanish name, and there wasn't much immigration from Mexico to New Mexico in those days).
http://www.nndb.com/people/894/000122528/ Meanwhile Senator Tom Apodaca's father was a Mexican from El Paso, Texas (probably a first-generation American).