First, you need to ask your employer in El Paso if they will even agree to withhold New Mexico state taxes. Given El Paso's location on the border, they might already do this for other employees, but it would be good to ask.
Second, New Mexico uses the same W-4 that you file with your employer for the federal withholding. Presumably, if you get a nice refund of federal withholding, you are likely to get a nice (albeit probably smaller) refund of NM withholding.
In any case, if you really really don't want to pay any tax at the end of the year, declare yourself as Single with no dependents for maximum withholding. It will likely be way too much (unless you really are single with no dependents), but you can adjust it with your employer for the year after.
The taxing authorities don't mind you giving inaccurate information on the W-2 if it results in your having MORE withholding done - after all, that's just an interest-free loan for them.
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