Europe and the United States have much in common in that their sovereign debt problems are really quite simple to understand. You don't need a PhD in economics-- you just need to understand basic arithmetic.
In the US, for example, the government does not collect enough tax revenue to cover even the most basic services that society deems sacrosanct: defense [offense], social security, and Medicare.
In 2010, the federal government collected $2.2 trillion in tax revenue and spent north of $2.5 trillion just on those three programs-- already $300 billion in the hole. Everything else-- the post office, Homeland Security, the FAA, the FDIC, even the light bill at the White House-- is funded by debt.
That includes the most peculiar debt-funded item-- interest on the debt. The US government has to borrow money just to pay interest on the money it has already borrowed. This is unsustainable, it's simple arithmetic.