One item which hasn't been mentioned:
Increasing purchasing power doesn't boost the economy. Only increasing productive power can do that. If people drain their resources faster, they have less to invest in the future. This can create a temporary boom, but inevitably results in a later bust. This is a large part of why we're in the present situation. Investors poured huge amounts of money into anything which ended in ".com", creating lots of high-paying jobs for a little while. Then the inevitable consequences of foolish spending hit.
A tax cut can help the economy, but not primarily by boosting consumer spending. My spending will stay low for some time in any case, while I try to catch up on my savings. A tax cut will help to the extent that it makes productive efforts profitable which wouldn't have been profitable before. Before complaining about this benefiting "the rich," ask how many jobs "the poor" are going to hire you for. If an employer expects a net gain in hiring you, you may get hired. If it looks to the employer like a net loss, because of taxes or any other reason, you won't.
There are other factors keeping the economy down, with fear of terrorism having been a big one in the past couple of years. A rise in dishonest acts by businesses has been a large factor; distrust puts a heavy brake on economic growth. Widespread dishonesty is a serious problem for which there's no easy fix. So a tax cut won't be a magic cure, but it will help.