Upon the date the new combined municipal organization begins operation as provided herein, and thereafter, the organization shall be a municipal corporation of New Mexico and thereupon and thereafter shall exercise all the powers vested in it by the charter adopted for its government and all powers and duties vested in cities by the constitution and laws of New Mexico, and also all powers vested by law in counties, except as provided in the charter adopted and in Article 10, Section 4 of the constitution of New Mexico.