As someone who spent the first decade of his career researching, teaching, and writing about the history of economic ideas, let me assure you that there is no such thing as a "trickle-down" theory. No economist of any school of thought has ever proposed any such thing.
Cuts in tax rates are intended to do what past tax cuts have done before -- under both John F. Kennedy and Ronald Reagan -- namely, cause an increase in real economic activity. In both cases, the government received more tax revenues, as a result of rising economic activity, than it had received when tax rates were higher.
That is why it is so misleading to express a tax cut in terms of so many billions of dollars. The government can only change tax rates. How much revenue will increase or decrease is something they will find out later.
Tax cuts should be immediate, if you want results to be immediate. Stretching out the tax cuts, as was done initially in order to get political support, gives people incentives to wait before investing. Waiting is not what you want.
The only people whose taxes can be cut are people who are paying taxes. This simple and obvious fact gets overlooked by those who are busy crying "tax cuts for the rich." Tax rates are so skewed that a relatively small percentage of the population pays a huge proportion of the taxes at any given time.
That ensures that any serious tax cut will qualify as "tax cuts for the rich" -- as defined by liberals. How they get away with this phony stuff is one of the mysteries of our time.