Many people forget that government debt is someone else's asset. That is, every government bond or treasury security out there is the government's IOU, but the holder's asset. So increasing government debt is increasing the non-government sector's assets or net savings. The non-government sector can't net save on IOUs/assets held against each other, so it relies on the government's securities to net save.
This means that the $16 trillion+ government debt is the world's net savings in the U.S. dollar of account. Since savings are good and since we would expect the economy to continue to grow, we should expect that savings and thus the debt will go up forever. This means 17, 18, 19 trillion and counting and that's a good thing! Not something to be worried about! So why are people worried about it?
Here are the usual arguments:
1) Bankruptcy
We know this is false and is easy to prove or show. The government can simply print more money to pay any debts it has promised to anyone. Now in practice they don't print much money to pay their bills, they just change numbers in bank accounts, but the basic idea is the same. They are the monopoly issuer of the U.S. dollar and can thus pay any debts denominated in U.S. dollars. In this way we are not like Greece. Greece's debts are payable in the Euro. They are not the monopoly issuer of the Euro. They cannot pay debts without accruing Euros first through taxing or borrowing. They can go bankrupt. They, again, are a currency USER.
The U.S. does not face those same difficulties as the ISSUER of the currency. They do NOT need to tax or borrow in order to spend. The only reason they do so is to limit the private sector's purchasing power in order to prevent inflation. If they didn't tax or issue bonds to drain the private sector's purchasing power, and spent the way they did, then we would likely have the third thing everyone is concerned about (see below).
2) Interest rates
Many are worried that the bond markets will turn on U.S. bonds by refusing to buy the U.S.'s debt and so interest rates will go up, like they did in Greece or Spain. This is a more hairy explanation, but the simple answer is that as a currency ISSUER, the U.S. doesn't face that possibility, that Japan is a better comparison, who is also a currency ISSUER and has had very low interest rates for over a decade.
The U.S. has had record high deficit spending and record low interest rates. The theory that makes people worry is that high deficits cause high interest rates because fear will grow over whether or not the government will be able to make good on its debts. After #1, we know it can always make good on its debts, bankruptcy is not a concern. It is possible that fear would still grow anyway, despite this most basic fact, but it is wholly unlikely and still has not come to fruition despite repeated warnings it will for several years now. Those who spend their life trading in markets know that U.S. debt is a safe asset to hold so long as they don't threaten to voluntarily declare bankruptcy (or stop making payments on IOUs it has promised), which they are doing unfortunately.
So, in sum, this hasn't been an issue and won't be so long as the US doesn't voluntarily declare bankruptcy, something it does not have to do, or otherwise threaten to not make promised payments. Unfortunately, this might be a tool used by either side to get their way on the new budget deal. And again, Japan has paved the way:
Japan Debt-to-GDP
Japan Interest Rates
Debt goes up, but interest rates go down in both.
U.S. Debt-to-GDP
U.S. Interest Rates
The proof is in the pudding. Interest rates are not going to go up without the voluntary and unnecessary threat to not pay its debts.