Germany's leader this week called for new rules that would allow for expulsion, and many people in debt-ridden countries like Italy and Greece are increasingly blaming the euro for their woes.
But monetary independence could be more curse than cure: against dreams of devaluing to cheapen exports and boost economic growth may be a starker reality of catastrophic capital flight and paralyzing administrative headaches.
At first glance, having control of your own currency may look like an appetizing proposition -- and ordinary people in the countries hardest hit by the crisis have been waxing nostalgic.
Nikos Kastriotis, a shop owner in Athens, said he would be delighted with the return of the drachma, which was the standard silver coin of Greek antiquity. The Greeks swapped their legendary drachmas for euros in 2001, two years after the original 11 eurozone members.
"We didn't have so much money in our pocket but at least we were sure of what we had," said Kastriotis, who has drachma notes on display in his shop.
In Rome, grocery store owner Flavio Garabello blames the euro for making things more expensive -- even though the single currency has been widely credited for keeping a lid on inflation, particularly in Italy.
"With the lira I just made it through the month; with the euro, at the third week of the month I'm already in trouble," he said.
In practice, however, leaving the euro would likely trigger an economic meltdown that would make newly fiscally independent countries long for the shackles of the common currency.
As well as being a costly administrative nightmare, investors would probably insist on sky-high interest rates to hold onto the drachma or lira instead of the euro -- hardly the route to long-term growth or a solution to the debt crisis.
In addition, it could trigger a bank panic if depositors take their money out for fear their euros will be redenominated in lower-rated national currency at any time. Investors would also balk at the idea of investing in a country whose currency's value could vanish overnight.
One argument cited by fans of a country having its own currency is that devaluation could be a tool in lowering the value of debt denominated in the national currency.
This may be relevant to countries like Iceland who are currently considering whether to join the euro and abandon their own currency. But they might prefer to heed economists who say devaluation is a bad strategy that would simply raise future borrowing costs.
And for Greece, an abandonment of the euro may actually make repaying the debt harder still: it's denominated in euros already, which means they would have to buy euros with a new -- and likely to be weak -- drachma to pay it off.
On the other hand, membership in the euro has many unseen benefits.
Jean-Claude Trichet, the president of the European Central Bank, argues that countries like Greece can borrow at much lower interest rates than they otherwise could and have immediate access to the deep pockets of the ECB.
For example, Ireland has suffered an extremely deep recession as its property bubble burst but it hasn't been pushed to the brink of bankruptcy like Iceland, partly because its economy has been cushioned by its euro membership.
Danai Logotheti, a retired tour guide in Athens, thinks it would be a disaster for Greece to drop the euro -- a development that would turn it into "just another Balkan country."
"Prices would still be really high and our currency would be worth nothing in the rest of Europe. To say we'd be better off is ridiculous," said Logotheti.
On Wednesday, German Chancellor Angela Merkel broached the subject of a shrunken eurozone, backing proposals that a member state could be forced out of the club for consistently failing to abide by its rules.
Though Merkel said the Greek government had "shown a lot of courage" in its attempt to get a grip on the public finances, she called for future rule changes to make sure the eurozone is not engulfed by a similar crisis again.
"We need to have an agreement in which, it is even possible as a last resort, to exclude a country from the eurozone if, in the long-term, it again and again fails to fulfill the conditions," said Merkel.
At present, there is no legal basis for expelling a country from either the European Union on the eurozone, though the EU can take sanctions against a country that's not playing ball -- voting rights, for example, could be suspended if EU principles are violated.
Greece has certainly stretched the boundaries of what is acceptable and not: creative accounting practices convinced its partners in the European Union that its public finances were under control.
That all changed last October when the new government, headed by Prime Minister George Papandreou, sharply revised the 2009 budget deficit to 12.7 percent of the country's national income from a 3.7 percent forecast months earlier. The euro's rule book, which sets a deficit limit of 3 percent, had never been flouted so much.
Though expelling a country is not an option, there is now a voluntary withdrawal mechanism -- albeit complicated -- from the eurozone enshrined in the Lisbon Treaty, which was finally passed late last year following a 'yes' vote in an Irish referendum and ratification in Poland and the Czech Republic.
It's unlikely that Merkel is really trying to orchestrate a Greek departure from the euro. Her comments have widely been interpreted as an opening gambit in the creation of a new euro framework to make sure that another debt crisis does not happen again in the future -- and a nod to a bailout-opposing German public leery of any role as rich uncle.
"She's playing a lot to her domestic audience and presenting the image of (Germany) not getting rolled over by the Greeks," said Simon Johnson, a professor at MIT and a former chief economist at the International Monetary Fund.
Either way, it is increasingly clear that the crisis has engulfed the eurozone has laid bare the time bomb ticking at the heart of the euro experiment: the lack of budgetary union alongside monetary union.
Experts say that in an ideal world a unified fiscal policy would be needed to prevent countries from running up massive debts that weigh on the single currency's credibility.
But given that the eurozone is not the United States of America and has 16 sovereign members, each with different temperaments, political complications and development levels, that ideal is unlikely to materialize anytime soon.
What Merkel is really aiming for appears to be more coordination and stricter enforcement of budgetary rules.