Here is the 'Thrift Savings Plan'. A fund-type savings plan for Federal civilian employees and referred to as a model in the study Bush keeps referring to.
http://www.tsp.gov/ See 'Fund Sheets' on the right by the Bull ( Hah! should be a Bear given how the Common Stock fund has done the last few years )
This currently totals about $130 Billion, a SS accounts plan would quickly exceed that.
All the funds have management fees of $1 per $1000 of balance, so $130 Million a year in fees for the current TSP plan. This includes the Govt bond fund - managed by "Federal Retirement Thrift Investment Board" and the others, which are all managed by Barclay's.
Barclay's is a U.K. based bank - a London bank. Not quite the same as wall street. So of the $130 Million a year, they ship $75 million or so overseas. So if it were private SS funds of say $5 Trillion, we would pay $5 Billion a year in fees and perhaps send a bunch of it overseas?
Bond funds (Fixed Income) are marketed as lower risk than Stock funds (Equities). But notice the return chart of the 'G Fund' versus the 'F fund'. The Board managed 'G Fund' has fairly constant returns tied to the interest rates of the bonds they buy. The Barclay's managed 'F Fund' sometimes has negative or zero returns.
How do you get negative returns by buying and holding bonds that pay fixed or at least positive interest? By speculating on interest rates, and constantly buying and selling selling bonds, sometimes at a loss. Not a whole lot less risky than stocks except you theoretically don't loose out as bad in a case of bankruptcy.