Consider Italy. It is no exaggeration to say that the fate of Italy is the fate of the euro zone: if Italy can keep its debt under control and its banking system solvent, the euro zone will probably make it; if Italy defaults, the resulting panic will probably force Portugal, Ireland, Greece, and Spain to follow suit.

This linchpin is under a great deal of strain. Italy’s public debt stands at $2.3 trillion, roughly 20 percent larger than the country’s GDP. If not for that debt, Italy would have run a slight budget surplus in 2011. But interest payments alone soaked up nearly 5 percent of the GDP, creating a deficit of about 3.6 percent of national income and increasing the debt even more.

This has left Italy incredibly vulnerable. For every percentage point that the interest rate on the debt increases, Italians have to divert another 1.2 percent of national income into debt payments. And because markets are worried about this problem, interest rates have been rising at a brisk clip, with only occasional pauses while the powers that be deploy yet another emergency rescue plan.

Sweating this debt down by austerity alone would take ages, cause immense suffering among people who depended on the cut services, and—as Greece has shown—draw fierce public opposition. Moreover, commentators like Paul Krugman argue that it would actually make the problem worse in the short term, because government austerity makes the economy contract. As they see it, trying to close Europe’s fiscal gaps with austerity alone is like trying to get out of a deep hole by digging harder.

Strong growth by Europe’s troubled debtor nations would of course offer a different, and less painful, way out. After all, if you make $30,000 a year, a $10,000 credit-card balance is crippling; but if you make $300,000 a year, it’s fairly trivial. The faster Italy’s economy expands, the more manageable Italy’s debt becomes.

But that’s where the dearth of workers comes into play. Everyone agrees that rapid growth would be much nicer than higher taxes and slashed pension payments. The hitch is that over the past five years, growth in the Italian economy hasn’t averaged even 1 percent a year. Soaring growth will be tough to achieve, because more and more Italians are getting too old to work—and fewer and fewer Italians have been having the babies needed to replace them.

Italy’s fertility rate has actually been inching up from its 1995 low of 1.19 children for every woman, but it is still only about 1.4—well below the number needed to replenish its population (2.1). As a result, even with some immigration, Italy’s population growth has been very slow. It will soon stall, and eventually go into reverse. And then, one by one, the rest of Europe’s nations will follow. Not one country on the Continent has a fertility rate high enough to replace its current population. Heavy debt and a shrinking population are a very bad combination.