What is the New Mexico tax amnesty I've heard about?
Once upon a time there was an tax amnesty program, now there is what amounts to another one. New Mexico's Tax Amnesty law expired September 30, 2010. However, there is still an opportunity to avoid penalties & interest if you qualify for a Managed Audit.

Requirements. The main requirements to qualify for a Managed Audit are:
  • Return(s) must not have been filed.
  • Returns may have been filed but need to be amended.
  • There is no unpaid tax debt not covered by an installment agreement.
  • An audit has not begun.
  • You have not been contacted repeatedly regarding the unfiled return(s). 
To begin. You must apply.

At the end. You must pay in full all taxes due on delinquent tax returns within 180 days of the date of the state's billing notice.

From start to finish a Managed Audit will take at least nine months.