They went ‘big time’ for Obama this last election.
You are confusing the San Juan Basin with, perhaps, New Mexico as a whole.
The San Juan Basin favored Romney in the 2012 election -- especially so in San Juan County, NM.
.......................Romney.......Obama
San Juan, NM.......28,849......15,855
Montezuma, CO....7,372.......4,486
San Juan, UT........3,006.......2,062
Apache, AZ..........8,250......17,147
Thus, the four counties in the basin voted for Romney (47.5K) over Obama (39.6K). The Navajo Reservation comprises most of the Arizona county, explaining their vote for Obama.
The Red/Blue map I saw distinctly had a large area around Four Corners colored in Blue. Or, maybe once again I’m the colors mixed up.