The bars in the above chart represent each earning brackets' share of total income (in blue) and share of total tax, and not merely income tax, contributions (in red). Matthew O'Brien explains why the system is only slightly progressive, despite 47% not paying federal income tax:
[T]here are lots of other taxes, and they're mostly regressive. The payroll tax and state and local taxes all hit poorer households harder than they hit richer households. Once you add up the progressive federal income tax and the regressive federal payroll tax – which raise roughly the same amount of revenue – with regressive state and local taxes, you only just get a progressive system overall.
Previous Dish on payroll taxes here.