Well, of course it's true - kind of. But just stating that there is nothing to worry about because you don't actually need to pay a bill until it comes due, and its possible you might win the lottery before then, is a pretty "Pollyanna-ish" view. The fact remains that this government is borrowing roughly 40 cents of every dollar it is currently spending.
We aren't paying for our debt now. We use accounting gimmicks to cover up the real costs and debase our currency to hide the actual interest costs.
If the Federal reserve were not buying basically all new debt issuance by the US government the interest costs on that 11.6T would sky rocket and the new debt added tho the balance sheet each month would be monstrous and growing at an ever increasing rate.
We are living a fantasy currently. Our debt SEEMS to be reasonable and that we can pay for it. But that fantasy will end and when it does all of those promises to pay for things that the government has made will disappear as well.
What is most likely to occur is that we will have a currency crisis - a hyper-inflationary event that destroys savings, destroys promises and wipes out the middle class and the upper middle class - the very people government always says they are trying to "help".
Add to that the reason for the upcoming possible sequester comes from a supposed stopper on spending and get the government spending under control measure for raising the debt ceiling! More debt, then fix it later, that's not a good way balance a budget.