We already have government supported (tax free) "private retirement accounts" . . . they are called IRAs and Keoghs.
We already have an old age retirement insurance program . . . called Social Security . . . for those who unfortunately put all their "private" retirement investment in Enron or WorldCom or WPPS bonds.
We have a modest long term problem with Social Security funding because of two "mistakes" . . . 1) we have capped FICA taxes and limited them to wage income instead of including interest, dividends and capital gains in the taxable base and . . .
2) we have "invested" temporary Social Security surpluses exclusively in the bonds of a now bankrupt government.
The twin solutions are simple and obvious. Remove the FICA cap and apply the tax to all income, and diversify the investment of Social Security "surplus" funds.