Social Security Payroll Tax is Very Progressive
Unfortunately for Krugman, the facts suggest otherwise. Andrew Biggs of The American Enterprise Institute presents those facts, including the chart above in this Enterprise post, which show that the Social Security payroll is extremely progressive, not regressive as Krugman suggests.
The bottom four quintiles (by lifetime earnings) pay negative net tax rates for Social Security, meaning that they receive more in Social Security benefits than they pay in payroll taxes. Only the top income quintile pays more in payroll taxes than they receive in Social Security benefits. The bottom income quintile gets the best deal of all, with a negative net payroll tax rate of almost 27%, meaning that their lifetime Social Security benefits far exceed the payroll taxes they contribute to the Social Security program.
Bottom Line: Just like the extremely progressive income tax (see CD post here), where the "bottom 40% make a profit from the federal income tax, meaning they get more money in tax credits than they would otherwise owe in taxes," the Social Security payroll tax is also extremely progressive - the bottom 80% make a profit from the program.