Why austerity budgets fail

We hear a lot these days about the need to cut taxes and cut services to make states more "business friendly" and grow the economy.
Seems like a good idea.
I know, I just paid my town taxes, it hurt to write the check.
I wouldn't mind if they were lower.
If they were lower, I would probably spend part of the savings and bank the rest of it. The part I would spend would stimulate the economy a bit.
The problem with this approach to stimulating the economy is multifold.

While I would slightly stimulate the economy with the extra spending, the rest of it would go to savings and do little towards stimulating.
If I paid less in taxes, some service would have to go.
Perhaps the roads would not get repaired or plowed as well.  Perhaps a teacher would be let go.
Besides the loss of these services, which I have said through my vote that I find beneficial, there would be a loss of income for the worker who previously provided that service which I believed in.
That loss of income would cause a loss of spending, and that decrease in spending would more than negate the economic stimulus that my slight increase in spending provided.
In addition, that worker would need assistance from me in the form of unemployment insurance, medical care, food assistance, etc.

So, in my attempt to stimulate the economy through a tax break, I would have caused a net decrease in spending and economic stimulus,
and,
increased cost to the town (and me) in the form of economic assistance to the person who used to provide the service that I wanted in the first place.

Kind of like shooting myself in the foot.

What if I took the opposite approach?

What if I took anyone in my town who was unemployed or underemployed and provided them with a job that paid a living wage and provided healthcare and other basic needs?

I would love to have an extra hand to help repair the potholes in my street or provide other needed service in my town.
At the same time, I would save money that I now spend on unemployment and other assistance.
But also, as far as stimulating the economy, the newly employed people would spend their newly earned money in local shops and stimulate the local economy. Those local shop owners would spend their increased income in other shops or investments in their own shops and the economic stimulus continues.

Perhaps ironically, by investing in people instead of giving myself a tax break, I would achieve an economic stimulus and the more "business friendly" state that I sought.

There is disagreement in what caused the Great Depression of the 1930s and what helped end it, but what is generally agreed upon, even in the difference of opinions, is that government spending played a positive role towards ending it, because it led to increased employment and the increased private spending that came with it.

This is the basis of why austerity budgets have the opposite effect that people seek.
People seek a boost to the economy and a decrease in taxes but because austerity budgets lead to higher unemployment and lower wage scales, they depress an economy and cause a loss of services and increases in taxes.
Legislators in Kansas and Illinois have recently overridden their governor's vetoes in a rejection of austerity budgets, not because they have suddenly become anti-business, but because they understand that austerity budgets harm the very goal of becoming "business friendly."