If you look at the two links in your reference document (
http://lnvb.westside.com/NewMexico/NewMexicoByCounty.ht... ),
http://65.160.159.96/County1.htm and
http://www.sos.state.nm.us/avrs/COUNTY.HTM, you'll see that the % is not "turnout". It just means that a lot of registered Democrats purportedly voted for Bush (which I think is the real mystery).
For example, Hidalgo County votes:
JOHN F. KERRY and JOHN EDWARDS Democratic 861 43.8%
GEORGE W. BUSH and DICK CHENEY Republican 1081 55.0%
Registered Voters:
Republican 665 22.41%
Democrats 2,132 71.83%
That Republican/Demo turnout percent is a useless number (unless there is data out there that says who voted for whom based on their party registration - but that's not in any of these links).
On edit - added the actual links and picked a better example county!