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You know, I almost wish they had tried:

NMSA 30-16-9. Extortion.  
Extortion consists of the communication or transmission of any threat to another by any means whatsoever
with intent thereby to wrongfully obtain anything of value or to wrongfully compel the person threatened
to do or refrain from doing any act against his will.   
Any of the following acts shall be sufficient to constitute a threat under this section:   
A.   a threat to do an unlawful injury to the person or property of the person threatened or of another;   
B.   a threat to accuse the person threatened, or another, of any crime;   
C.   a threat to expose, or impute to the person threatened, or another, any deformity or disgrace;   
D.   a threat to expose any secret affecting the person threatened, or another; or   
E.   a threat to kidnap the person threatened or another.   
Whoever commits extortion is guilty of a third degree felony.

Kidnapping is defined in the NMSA as:

30-4-1. Kidnapping.  
A.   Kidnapping is the unlawful taking, restraining, transporting or confining of a person, by force,
intimidation or deception, with intent: 
(1)   that the victim be held for ransom; 
(2)   that the victim be held as a hostage or shield and confined against his will; 
(3)   that the victim be held to service against the victim’s will; or 
(4)   to inflict death, physical injury or a sexual offense on the victim. 
B.   Whoever commits kidnapping is guilty of a first degree felony, except that he is guilty of a second
degree felony when he voluntarily frees the victim in a safe place and does not inflict physical injury
or a sexual offense upon the victim.

Likewise False Imprisonment:

30-4-3. False imprisonment.  
False imprisonment consists of intentionally confining or restraining another person without his consent
and with knowledge that he has no lawful authority to do so.   

Whoever commits false imprisonment is guilty of a fourth degree felony.

All that leads to the keystone, Art II, Sec 6 of the NM Constitution:

[Right to bear arms.]
No law shall abridge the right of the citizen to keep and bear arms for security and defense,
for lawful hunting and recreational use and for other lawful purposes, but nothing herein shall be held to
permit the carrying of concealed weapons. No municipality or county shall regulate, in any way, an incident
of the right to keep and bear arms. (As amended November 2, 1971 and November 2, 1986.)

Thus their 'law' would be born stillborn, they would be guilty of extortion and conspiracy, and it would be a great chance to clean out government.

Of course that's all resting on the possibly false assumption that the law means what it says and is not merely "for display purposes" (with real authority being derived from power).