Yes they do all states have the EUC extensions. New Mexico as of now can get 20 weeks of EUC extensions after they exhaust their regular 26 weeks of state benefits. EUC does go to 33 weeks but NM has to have a TUR at a three month average at 6% or higher which they don't have yet. New Mexico's TUR as of now for a three month average is only 5.1%.