The problems caused by rising debt are fundamentally different in the U.S. from those in Europe, but they are equally daunting.

Christophe Karaba / EPA French President Nicolas Sarkozy and German Chancellor Angela Merkel (L) hold a press conference, in Cannes, France, Nov. 2.

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Throughout the richest parts of the world, rising debt and aging populations are causing economic instability. In Europe, of course, this problem has developed into a crisis that just keeps getting worse and from which the common currency zone is unlikely to emerge intact. It is only natural to wonder if similar structural economic problems are inevitably driving the U.S. in the same direction.

The short answer is no – at least not inevitably. But it’s crucial to understand why, because failure to address the very real problems America does have could eventually cause a lot of damage nonetheless.

Europe’s troubles are the result of past debt, some of which is now compounding at such high interest rates that for all practical purposes it can never be paid back. Call it a problem of arithmetic. The U.S., by contrast, is still years away from a debt crisis of the same magnitude. But it is having great difficulty getting its current budget under control. America’s problem, therefore, is not mathematical but political.

In one way, national debt is like credit card debt: If the interest on existing debt becomes greater than the monthly payment people can afford, the debt never gets paid off. It just grows and grows until it reaches the maximum amount that lenders are willing to provide. For countries, the equation is a lot more complex, of course. For starters, the interest rates countries pay are far lower than what credit cards charge. If interest rates are only 3% or 4% and the current budget (before interest) is more or less in balance, then economic growth may be enough to keep debt constant as a percentage of a country’s economic output (GDP). Such a situation can be stable indefinitely even if the debt level is fairly high.

(MORE: What the Greek Debt Crisis Means for You)

Once investors begin to fear that a country may default on its debt, however, a vicious cycle takes hold. Interest rates soar, which in turn makes the debt compound faster. And that, in a sort of self-fulfilling prophecy, further increases the chances of default. This is exactly what has been going on in Italy.

Europe’s common currency only makes this cycle more vicious. Typically, an overindebted country would see its currency decline in value relative to other currencies, which would help its economy by lowering labor costs compared with those of other countries. Such a policy would typically be accompanied by higher inflation that would also reduce the real value of the country’s debt (in terms of the amount of goods that the money could purchase).

The euro, however, prevents such a devaluation from taking the pressure off a troubled economy. That only increases the risk of an eventual default and makes bond investors demand higher interest rates. Once interest rates climb above 7%, as they have recently for Italy, a debt spiral is hard to avoid.

Since the euro also directly links the economic fate of 17 out of the 27 countries that make up the European Union, Europe will probably be unable to escape some sort of broad default crisis. When this occurs, no matter how well it is managed, major banks will take losses on their bond portfolios. That could trigger a short-lived selloff of as much as 20% in stock markets around the world, according to bearish forecasters.

Equally serious, banks would probably respond by cutting back lending, thereby squelching the growth essential to recover from the default. Indeed, forecasters in Europe are already reducing their growth projections and warning of a possible double-dip recession.

For America, the picture is both better and worse. On the plus side, we have plenty of time before our debt reaches dangerous levels. If debt at 60% of GDP is no problem and 120% is Italy, we’re still below 100% (and roughly one-third of that is money owed by one part of the U.S. government to another, as with Social Security, which means it doesn’t really count). Moreover, because the U.S. is so big and so rich – and because we control our own currency, which is still other countries’ first choice for their foreign reserves – we can support proportionally more debt than Italy. As a result, we are still able to borrow at less than 3%.

(MORE: Why France — Not Greece or Italy — Will Decidee the Fate of the Euro)

On the minus side, we have not been able to get our current budget under control the way most European countries have. Thanks to recent budget cuts, Italy is now running no annual deficit (if you don’t count interest costs), while ours is a whopping 7% before interest costs. Economists such as New York Times columnist Paul Krugman will tell you that austerity is not the answer, that we need stimulus to get out of the current slump, but that is only half-right. What we need is short-term stimulus and long-term spending cuts. What we have is exactly backwards – debates over near-term austerity combined with unconstrained long-term deficits.

It may be true that taxes should be raised, that defense can safely be reduced and that the discretionary Federal budget can be trimmed. Doubtless the Congressional Super-Committee is debating such matters and we shall hear the fruits of their deliberations in the next two weeks – or not. But whatever savings these negotiations produce, they will likely fail to slow the biggest cause of long-term deficits – growth of entitlements.

Among all the entitlements, Social Security is the easiest to stabilize. The real intractable problem continues to be healthcare, including Medicare, Medicaid, Veterans Benefits and such. With rising medical costs and an aging population, it is hard to see what the solution would be, especially since recent health-care legislation has not slowed rising costs, and the prospect of reopening the health-care debate is hardly encouraging. Although we still have plenty of time to fix things, the political challenges look daunting indeed.

How long does the U.S. have to sort these problems out? Debt could reach Italian levels in 10 to 12 years under what the Congressional Budget Office calls the Alternative Fiscal Scenario. Moreover, the oldest Baby Boomers just turned 65 and have a life expectancy of 22 years. That means the bulge of retirees will keep growing and won’t start to shrink until after 2030. So the risk of a European-style crisis won’t go away on its own. If we don’t face up to our debt problem, there’s a lost decade just waiting to begin not too far in the future.