Yes, the poor will spend most of their income on consumables. The rich also consume, often in larger portions. Someone has to build that yacht or fancy house. The rich can also save their money (which is borrowed by individuals and businesses) or invest it themselves (giving to a business). In the end, all money is put to use in the circular flow.
Economically, it isn't enough for 'someone to spend something', it's the rate of reinvestment. If the rich only spent ten or twenty percent, sure it's a larger portion than if someone poor spent ten or twenty percent, but what economists measure is the 'return on investment' (i.e. the tax giveaway). With payments to the 'working poor', there's a clear history of a seven-fold increase. Giving money to the poor, there's a less than 10% reinvestment rate. Sure, they can 'invest the money', but there's no guarantee it'll even be in this country (think it being deposited in the Cayman Islands).
Every time anyone mentions tax reform, they bring up the old 'the rich pay more money than the poor', but that's NOT the money that makes the financial investment (in pay cuts) pay off.
I worry that tax rates that are too progressive discourages people from trying. When the top marginal rate was 91%, why even bother to make that much money? The extra money in the pocket is less than the extra effort expended.
Yes, that is an issue, but it's mainly a question of what is a worthwhile tax give-away. Lowering the tax rates sounds nice, but as we're seeing, that typically only amounts to moving it from one person's pocket into another person's pocket, and thus you're once again playing favoritism, rather than benefiting either the public or the economy.
I should also point out, the one way to spend money which has guaranteed results, is funding the IRS to investigate tax fraud, yet the U.S. has continually defunded the IRS for a long-time, to the point they can't allocate the personnel to check cheating. Paying the IRS would generate a LOT more direct revenue than large tax giveaways to the wealthy, but that doesn't reward those who fund political campaigns. Also, defunding the IRS means the few auditors they have are more likely to audit the small mom & pop business than the major corportations and hedge funds that employ hundreds of accountants and lawyers to fight any active investigations—once again resulting in increased losses to the economy and bigger benefits to those who offer no real advantages in the investment (aside from future campaign funds).