The problem is this: once you have a high level of debt, you become sensitive to interest rate changes. Your debt rises, so you have to increase interest rates to lure investors to buy the bonds. The high interest rate forces to you run a bigger deficit, do you have to borrow even more money. Then investors demand an even high risk premium. That's the cycle.
Once that process takes hold, the only way out is some combination of lower living standards, higher taxes, higher inflation and currency devaluation.
You're right that it hasn't happened yet in the modern era. But it will. Remember where you heard it first.