Those who need a "tax cut" most don't pay any taxes. What you're talking about is income redistribution, not a tax cut.
They pay taxes, just perhaps not income tax. In addition, there are people who badly need tax cuts who belong to a lower income tax bracket. To me, I don't care if a millionaire has an extra 20 grand or not, but I do care whether my 20 neighbors have an extra 1 grand each.
It's not always a choice between helping the poor and helping the economy, I think the progressive income tax does both.