Poor people spend all of their income, so all of it would be taxed. Rich people do not spend all of their income, so they would pay a lower tax percentage. However, such a tax would encourage savings. There are problems with collection and avoidance. VAT schemes address some of the issues. A way to accomplish something like the proposers think they want would be an expenditure tax, and it could use the existing IRS infrastructure. To understand more, read Nicholas Kaldor.