This single widely accepted assertion, tells us a lot and answers many of the questions asked here.
It means that before we can predict the impact of a federal government deficit we have to know who is receiving the deficit spending money. If the money is going to the rich we will have more savings in the economy and more wealth accumulated by the rich. If the deficit is spent so that the non-rich receive it we will have more spending in the economy. Simple.
Tax cuts create deficits that put money into the hands of the rich. Tax cuts reduce revenues, creating deficits, and don't change, i.e. increase, government spending.
Deficit spending puts money into the hands of the non-rich. That is, infrastructure spending creates jobs that pay wages. Transfer payments go to the non-rich, contribute to the budget deficit and are spent on consumption, creating jobs and adding to wealth of the non-rich.
The rich save their money received from the tax cuts by buying government bonds, buying stocks in the stock market, buying real property or just putting it in a bank account, increasingly in offshore tax havens. The money is saved by the rich, in no meaningful way is it invested in the economy. It effectively leaves the economy.
This is the reason that tax cuts don't stimulate the economy, the physical economy of making things and providing services. The economy that the vast majority of people depend on for their livelihood.
It does stimulate the paper economy of stocks and bonds, of money sitting in a bank account.
