(a)   Notice and hearing.  The board of mayor and aldermen shall publish a copy of the proposed budget, a notice stating the times and place where copies of the message and budget are available for inspection by the public, and the time and place for a public hearing on the mayor's budget as submitted, at least one week in advance of the public hearing.
   (b)   Amendment before adoption.  After the public hearing, the board of mayor and aldermen may adopt the budget with or without amendment. In amending the budget, it may add or increase programs or amounts and may delete or decrease any programs or amounts, except expenditures required by law or for debt service or for an estimated cash deficit, provided that no amendment to the budget shall increase the authorized expenditures to an amount greater than total estimated income and provided that no consolidation of city depart-ments shall be accomplished solely in the budget process without separate and specific additional action by the board of mayor and aldermen. If amendments are made to the budget submitted by the mayor, a second public hearing may be held providing public comment on the changes made, prior to the final adoption of the budget.
   (c)   Adoption.  The board of mayor and aldermen shall adopt the budget on or before the second Tuesday in June of the fiscal year currently ending. Such adoption shall include such appropriation and revenue ordinances as shall be required to fund the budget adopted. The power of the mayor to veto acts of the board shall apply to the entire budget or any line item thereof stating the specific reasons for the objection and the proposed alternatives to the item vetoed, subject to the power of the board of aldermen to override. In the event of the exercise of a line item veto all portions of the budget not so vetoed shall be passed. (As used herein “line item” shall mean any object of expenditure listed in the budget.) The school department budget shall constitute a single line item. Action by the board of aldermen on any veto shall be completed by June 30. The final adoption of the budget shall require, subject to the veto powers of the mayor, the vote of eight members of the board of aldermen.
   (d)   If the board of mayor and aldermen shall fail to adopt appropriation resolutions for the ensuing fiscal year as provided herein, the budget as originally submitted by the mayor shall become the budget.