One of many references to the Social Security “Trust Fund”:
http://www.usatoday.com/news/washington/2005-02-28-trust-fund_x.htm
The actual physical repository was not set up until fairly recently ... 1994 perhaps.
Fundamentally, we are both correct. According to the article there are two trust funds, the money paid out is borrowed, but keep in mind with my simple x / y graph argument that there is way more being paid out than coming in.
So either they would need to cut benefits, drastically increase the amount taken from paychecks towards social security or what is likely to happen in typical government fashion. They print more money and the US becomes Greece, because the politicians don't want to cut the hand outs.