The Mayor has indicated that his administration has used Zero Based Budgeting (ZBB) as a method to insure that everything in the budget has been properly reviewed and justified. In other words, there is no need to question what has been included in the budget.
But Zero Based Budgeting, in itself, does no such thing. Traditionally, a new budget was based on the old budget or actual spending with some adjustment for inflation. In other words, everything that was in the old budget was in the new budget plus whatever new things were added.
ZBB means you start with a blank page and then you list all of the activities that you want to accomplish and their cost in the order of priority.
Once you know what you can afford to spend, add up the activities and their cost in order of priority until the total of the activities equals the total that can be spent.
If the Mayor did do proper ZBB then all of the activities should be detailed with their cost. If the items requested in the override could not be covered in the context of the non-override budget, then it means that there must be higher priority items in the budget.
It would be interesting to know which of the lowest priority items, in the budget, total the amount of the proposed override. Perhaps those items could be postponed or eliminated so that the override was unnecessary.