N.M. Stat. § 73-11-42
The assessor-collector, in person, or by deputy, shall attend at the courthouse in the county on the day specified in the notice of sale of property hereunder, and shall, between the hours of 10 o'clock in the forenoon and four o'clock in the afternoon, offer for sale, separately and in consecutive order, each parcel of property included in the list attached to the order of sale, or so much thereof as may be necessary to realize the amounts due. The same shall be continued from day to day until all the property described in the notice of sale, shall be sold, or until the amounts due shall be paid or realized. In case any property ordered to be sold be in too large tract or tracts to be conveniently sold, then the assessor-collector shall offer the smallest tract in acres for which any one shall bid the amount of tax and penalty, such tract to be as nearly as may be square body beginning at the northeast corner of the whole tract. In case the property sold shall realize more than enough to pay the amount due, the surplus shall be paid over by such assessor-collector, to the owner of such property. Each lot or parcel of property offered for sale shall be struck off to the best bidder for cash; but if there should be no purchaser in good faith, bidding upon the same, the whole amount of the property assessed shall be struck off to the district as the purchaser and the duplicate certificate delivered to the treasurer of the district and filed by him in his office after having the same recorded in the office of the county clerk of said county, and the assessor-collector shall make an entry "sold to the district" on the tax roll opposite the tax and shall be credited with the amount thereon in his settlement.
NMS § 73-11-42