Dean Baker objects to means testing Social Security here.
But, why not do the sensible thing and give all citizens above some age the same benefit? If I understand their Government speak correctly, that is what the Government part of the pension system in Australia does.
Social Security is already progressive see here, so why try to keep the voters deluded, thinking it is not welfare?
You could set the payment at $200/week/person, that would give the neediest a raise. I think this would reduce the total cost by about 30% which would mean that you could lower the tax allowing the citizens to spend that money when they choose to rather than in their older years. My Grandmother told my father spend the money when you are young and can still enjoy it.
Social Security is welfare program that was disguised as a Ponzi scheme to make it past the voters. Time to admit to them that it is and has always been a welfare program.