Whenever a petition is presented to the director which has been signed by 2,000, or more, of the total producers in the state, not more than six months prior to its presentation to the director, the director shall conduct a referendum among producers to ascertain whether they favor the carrying on of a voluntary promotion and research program for beef as prescribed in Section 64661. At the time any person starts to circulate such a petition, he shall notify the director of such action. The director shall establish the period of time during which such referendum shall be conducted which shall be not less than 30 days nor more than 90 days.