The American economy has been moving from a manufacturing economy to a service economy. The unskilled factory laborer in the Third World will always out-compete the unskilled American factory laborer. Higher taxes and the reduced profit margin they bring compounds the problem for American businesses.
A reduction in income taxes will not, by itself, increase the spending power of the poor as the poor pay little or no taxes right now.
An income tax cut, however, do create incentive for American small business owners. If you have high labor costs and the Government takes away a hefty chunk of the profit margin, there is little incentive to invest in small business which is the backbone of the American economy.
Europe has a dilemma right now because the high tax rates are driving people, including those who could be creating jobs with their small businesses, into early retirement.
I think the cuts were designed to allow this last group to invest as wisely as they could which will allow America to obtain as large a sector of world production of goods and services as possible. It seems that this strategy worked because tax receipts are up even though domestic private sector employment isn't.
I don't think there was any other way to stimulate the economy.
The down side is that the pressure on compensation for American workers (wages plus benefits) increases.