First, the idea that the lowest income earners pay so little in taxes is actually a bit disingenuous. People don't even realize what we really pay in taxes in this country. We see the income tax because its right there on our pay stub. But we also pay a ton of nickel and dime taxes on everything from cable service, to gas and other products that are assessed additional taxes on top of sales tax. The poor are not exempted from these taxes, at least not many of them. If they pay for cable service, they pay the exact same rate as the wealthy. They pay taxes every time they guy gas, or buy cigarettes. When all taxes are taken into consideration, the poorest among us can still pay as much as 20% of their total income in taxes. Imagine paying up to 20% of your income in taxes, fees, surcharges etc, when you only earn $14K a year. Easy to see why the lowest income earners contribute such a tiny percentage of the overall tax revenues, yet still pay their fair share.
With regard to a flat tax system, first there have been several proposals, each structured slightly different, so its difficult to speak in specifics. However, most flat or fair tax proposals involve implementing a national sales tax, and eliminating the income tax system altogether. There are numerous problems with implementing such a system.
1. A national sales tax won't eliminate the IRS. Indeed, the IRS would either need to be massively expanded, or new agencies created. In addition to an agency dedicated to collecting the nat'l sales tax, every proposal includes some form of "prebate". Citizens would still declare their income to the IRS, and from that, the amount of their monthly 'prebate' would be calculated. More than half of all Americans would receive a monthly prebate check cover all, or a portion of, the taxes they would pay in a given month. No more sending out a refund check once a year, the IRS would now be tasked with sending out millions of checks every single month. The progressive tax system lives on! Errr, sort of.
2. Some proposals for fair or flat taxes make an attempt to account for income allocated to investments, but most don't. You are taxed only on the income you actually spend. So not only would the highest income earners see their taxes slashed dramatically, dropping from as high as 38% down to 25%, a huge portion of their income would not be taxed at all. This is why a flat or fair tax would amount to a massive tax cut for the wealthy. Our gov't has proved unequivocally that they are incapable of reducing spending, so the massive drop in revenue would either need to be made up by lower income earners, or would simply increase our debt exponentially.