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Moreover, the US has a large current account deficit issue; the total volume of money they spend on buying things produced elsewhere is quite a bit larger than what they manage to bring in with things they've produced domestically (unsurprising given that the US manufacturing base has largely been shipped overseas).  If you look at the average household debt in the US, you realize that most families in the US are doing this spending using credit.

So you have a scenario where the US is exporting money via its current account deficit and spending beyond its means, generating large amounts of debt.  This works because the debt is being paid for by foreign central banks, most importantly in Japan, South Korea, Taiwan and China; and because the US dollar is an international standard reserve currency and the standard currency for sales of things like oil.  As long as this is the case, everything's fine.

If the US dollar stops being the standard currency -- for instance, if  OPEC starts selling oil in Euros, like Iraq was about to do before the US invaded -- or if central asian banks stop being interested in buying the US debt, then a very unfortunate chain of events is kicked off.  The dollar starts to depreciate.  Foreign central banks stop being interested in underwriting the US national debt.  The US finds it harder to buy foreign imports, because the US dollar isn't as intrinsically valuable (people increasingly don't see value in holding US currency, so the problems of converting it to Euros or whatever start to become more important).  Inflation picks up.  Because imported goods are getting much more expensive, and not much is produced domestically anymore, US consumers can't consume like they used to; the people backing all the credit US consumers have been spending with stop making money, so they raise their interest rates, making everything worse, and dropping the dollar even farther.  You get caught in a runaway cycle that just keeps getting worse and worse.

I'm not particularily well educated when it comes to economics, but I've seen the above scenario postulated by people who certainly are, and I haven't seen anything approaching a reasonable explanation of how you can continue to spend massively in excess of your income and buy continuously on credit.  If someone can explain to me where I've got this wrong, I'd love to hear it.

As for paying off the debt, it's certainly doable.  They'd have to roll back Bush's tax cuts, stop burning money in Iraq and be financially conservative for a while, but right now they seem to be doing their best to add to it as quickly as possible.  Why are they doing this?  Why isn't this a bigger issue in the US?  I have no idea.
 

7.6 trillion is an abstract number. We have no experience to relate to it, all we know is that it's big. 7.6 trillion spread between 400 million people (not exactly the population of the US, but it makes the math easier) gives $19,000 per person. That's a more comprehensible number, and is probably why I've seen national debts broken down into "per person" amounts as a way to explain them.