The problem with a flat tax is that is disproportionately favors the rich and directly hurts the poor, which is why so many of the people at the top trying to drum up support for it are wealthy people, and the grassroots support is poor to middle class people who aren't great at math and who hate going to H&R Block every year. Currently our progressive tax system is as follows for 2013:
Married Filing Jointly or Qualifying Widow(er) Filing Status
[Tax Rate Schedule Y-1, Internal Revenue Code section 1(a)]
10% on taxable income from $0 to $17,850, plus
15% on taxable income over $17,850 to $72,500, plus
25% on taxable income over $72,500 to $146,400, plus
28% on taxable income over $146,400 to $223,050, plus
33% on taxable income over $223,050 to $398,350, plus
35% on taxable income over $398,350 to $450,000, plus
39.6% on taxable income over $450,000.
Say you split the difference there between 40% at the top and 10% at the bottom, and set the flat tax rate at 25%. For a family making minimum wage every year, that's a yearly income of $15,080/yr. Take away 25% of that in taxes, and they're out $3,770 instead of $1,508. That's $2,262 more than they would be paying under the current system. On a monthly basis, that's $189/month less over the course of the year, for people living at or below the poverty line. That's a monthly food budget right there, poof gone. People at that income level tend to spend whatever they make, the majority of it on necessities like food and utilities, so you'd be taking that money out of the local economy.
Meanwhile, for the CEO making $450,000 a year, suddenly he's paying $112,500 instead of $178,200. He's paying $65,700 less than he had been, of course he's going to put his money behind lobbying for a "flat" or "fair" tax. It's much more fair... to him. Is he going to use that to hire more people? Of course not, because that's coming from personal income, not corporate income, and he doesn't get a tax break for it. Is he going to spend it in the local economy? Maybe, in the local economy where his yacht is parked in the Bahamas or around his ski chalet in Switzerland, but it's much more likely he'll put it into stocks and just make more money for himself with it.
Or say you don't base it on income at all but on a kind of sales tax. This would push prices up much higher, create a thriving black market, and still punish the poor and middle class because the *basics* you need to buy are the same no matter your income level.
It's impossible to have a "flat tax" that doesn't punish the poor and reward the wealthy. That's why the wealthy keep trying to convince you that you want it.