Your analysis would only be true in the absence of inflation. While for the moment we are in a mildly deflationary cycle, the only way that the $107 trillion in obligations of the government will be liquidated is through massive inflation. That inflation is probably not far off - perhaps five to seven years. Perhaps not that long...
Of that $107 trillion you quote, $13 trillion is for fixed dollar amount of bonds which we can print up a small stack of billion dollar bills and pay them off (along with the associated hyperinflation). The rest is primarily for Social Security and Medicare which are not fixed dollar amounts. Print up those billion dollar bills to inflate away the current debt and suddenly the average doctor's bill is in the millions of dollars for an office visit and the future obligations are in the quadrillions or quintillions of dollars instead of "mere" trillions.