So its not tax cuts brings prosperity/deficit reduction, but rather tax cuts and govt cuts in spending?

If you want to eliminate debt, end fiat based currency. The ability to create more debt out of thin air is too great a temptation to abuse. No amount of taxation or spending cuts will fix the problem. Every country in the world is deep in debt, all use fiat currency, some tax a lot, some don't, and some spend a lot and some don't.