We know that the Federal income tax is progressive, while the payroll tax is regressive, and that these are the main two sources of Federal tax revenue (around 81% in 2012).
The TPI has some interesting stats about the overall progressivity of the Federal tax system.
First, the lowest quintile (20%) of earners pay almost no Federal taxes. Their average income tax rate is negative and almost completely offsets their payroll tax rate. They earn around 4% of income and pay around only around 0.2% of Federal taxes.
Second, the highest quintile of earners earn around 53% of total income and pay around 68% of all Federal taxes.
Before seeing these numbers, I would have said that the regressive nature of the payroll tax makes overall Federal taxes much less progressive than the income tax. But it turns out that the overall Federal tax burden is (too my mind at least) still pretty progressive.