Though it is true that over 46% of American households pay no federal income tax, a percentage that grows during bad recessions and after generous tax cuts like President Bush's, it is not true that they pay no tax at all.
In fact, a quick inspection of the table above reveals that after considering all federal, state and local taxes, the poorest 20% of households pays a full 17.4% of their paltry incomes in taxes, not much less than the 28-31% paid among the richest groups.
The biggest reasons for this apparent regressivity is the cap on FICA payments and the relatively large share of sales tax that the poor pay, as they consume a larger proportion of their incomes than the rich.