The problem for a country like, for instance Spain, is that their current account balance has gone highly negative. This can be due to government overspending or private overspending and contraction.
In fact Spain didn't have a big public debt problem before the crisis. Their problems stem mostly from contraction of the private sector.
If Spain had its own currency, the current account deficit would create a surplus of peseta on the international markets and drive up the price of imports for Spain, while making products produced in Spain cheaper and easier to export. Devaluation would cause short term pain as Spaniards find themselves unable to afford foreign goods but long term prosperity as it would allow their economy to require its footing through favorable export terms.
The Euro itself won't be devalued as long as Germany retains a current account surplus. Ironically a very substantial part of Germany's surplus is exports to the so-called "PIIGS."
In the US we have examples of winner and loser regions due to our common currency. Witness: Michigan vs. Georgia. The situation here is different though because money can still flow into a loser state like Michigan through the federal government (social security payments, for instance, and highway funds). And most importantly Americans are highly mobile; Michiganders can head off to Chicago or Atlanta so while the prospects for Michigan itself remain bleak, people aren't trapped.
The people in the "PIIGS" countries are facing a truly bleak future. The Euro system has denied their countries the tools needed to recover on their own. And the practical realities of (the lack of) labor mobility in the Euro zone mean the people are trapped.