Both Greece and Italy (possibly also Spain and Portugal) share the same fundamental economic problem that is productivity and terms of trade. Simply put, they cannot compete on the international market in some sectors, with the exchange rate of the Euro, their real wages and price level.
A pre-euro Italy would look like this:
Competition from China→Pworld↓textiles
Real price = w/productivity
q= ↓E(pWorld ↓)/PItaly ↓)=>q ↓=>demand ↓
Increase demand through G↑ Mainly Italian products. But a restricted GDP ratio.