After receiving the budget submitted by the Mayor, and prior to taking action on the budget, the Council shall hold a noticed public hearing. On or before June 1, the Council shall:
(a) approve the budget as submitted by the Mayor; or
(b) modify the budget by disapproving in whole or in part any items, or by increasing or decreasing any item, or by adding new items, and return the budget as modified by the Council to the Mayor. Any action taken by the Council under this section shall be taken by a majority vote of its members.
Upon failure of the Council to return the budget to the Mayor as provided in this section, the budget as submitted by the Mayor to the Council shall be signed by the City Clerk and thereupon become the general City budget for the ensuing fiscal year.