If the Budget is voted down, it does not mean they are going to make a new budget with the desired results. They will more likely run an austerity budget which will make cuts and many people wont like.
There might also STILL be a tax increase, even with the budget being voted down as some things have to be paid for no matter what, like electric bills , heating bills , negotiated teacher salaries etc.
and just an fyi Gym , Art and Music are mandated by the state. Just because many yeshiva kids dont have some of these things , doesnt mean its not mandated or important