Different economists have different perspectives on how tax cuts will help to revive an economy. One set of economists believes that tax cuts can help to increase aggregate demand (AD). The other set of economists believes that it is better to use tax cuts to help increase aggregate supply (AS).
In the Keynesian perspective, the point of tax cuts is to increase AD. In this view, tax cuts should go mainly to the middle class and below. This is because these people are the vast majority of the populace and have the bulk of the buying power. When the government reduces taxes on these people, they will have more money. They are likely to go out and spend that money on things that they need. As they buy more goods and services, AD rises and gross domestic product rises as well.
From the supply-side perspective, this is not the right way to revive the economy. Supply-siders believe that an economy is best stimulated by increasing AS. From this point of view, taxes should particularly be cut on businesses, on investment, and on the rich. When these sorts of cuts are made, more investment is likely to happen. The rich will save money and will invest it. Businesses will save money and will put it into expansion. All of this will mean that more goods and services can be produced. That means that AS will rise.