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One reason current law won't allow Social Security to promise all the benefits that have been promised is that FICA revenue is projected to decline as a share of GDP over the decades. This is because though the FICA cap is indexed to inflation, rising income inequality means that each year a higher and higher proportion of total payroll income falls above the cap. We could fix that with an ad hoc adjustment, switch the index away from the CPI and toward a fixed proportion of payroll, or just eliminate the cap altogether (and lower rates accordingly) and that would eliminate the "perpetually growing" element of the infinite horizon deficit without making the tax burden on future generations any higher than what we're paying today.
The FICA cap is pegged to the wage index already. While the proportion of GDP escaping the clutches of the FICA tax is increasing over time, it's largely because of disproportionate increases at the upper end of the income distribution relative to the median... and, to add, rising nonwage income...