When Treasury Secretary John Snow was questioned on this issue he stated that the 'pieces of paper' are backed by the US. government.
You said that an entity cannot owe money to itself, but an entity was able to borrow money from itself, or in this case from the working people who paid higher taxes for twenty plus years. For Hillary to say that there was a surplus when Bill left office appears rather disingenuous, the surplus was due to the 1 Trillion dollars that had been borrowed from the SS Trust Fund.
I do not remember hearing too many elected officials talking about borrowing from the SS trust fund as they were voting for and continuing to fund the recent war.
Echoing Bush, conservatives claimed Social Security trust fund is a "myth"
http://mediamatters.org/items/200502040009"...A January 10 New York Times editorial explained:
In suggesting that 2018 is doomsyear, the president is reinforcing a false impression that the trust fund is a worthless pile of I.O.U.'s -- as detractors of Social Security so often claim. The facts are different: since 1983, payroll taxes have exceeded benefits, with the excess tax revenue invested in interest-bearing Treasury securities. (An alternative would be to, say, put the money in a mattress.) That accumulating interest and the securities themselves make up the Social Security trust fund. If the trust fund's Treasury securities are worthless, someone better tell investors throughout the world, who currently hold $4.3 trillion in Treasury debt that carries the exact same government obligation to pay as the trust fund securities. The president is irresponsible to even imply that the United States might not honor its debt obligations.
Similarly, Princeton economist and New York Times columnist Paul Krugman explained on December 7, 2004, that claiming that the General Fund does not truly owe its apparent debt to the Social Security trust fund amounts to arguing for a large income transfer from working-class Americans to the wealthy:
Right now the revenues from the payroll tax exceed the amount paid out in benefits. This is deliberate, the result of a payroll tax increase -- recommended by none other than Alan Greenspan -- two decades ago. His justification at the time for raising a tax that falls mainly on lower- and middle-income families, even though Ronald Reagan had just cut the taxes that fall mainly on the very well-off, was that the extra revenue was needed to build up a trust fund. This could be drawn on to pay benefits once the baby boomers began to retire.
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If the trust fund is meaningless, by the way, that Greenspan-sponsored tax increase in the 1980's was nothing but an exercise in class warfare: taxes on working-class Americans went up, taxes on the affluent went down, and the workers have nothing to show for their sacrifice."