A single currency could no more subsume national identities than drinking Coke could make people American. If other euro countries (Portugal, Spain, Italy) suffer Greece's fate -- lose market confidence and can't borrow at plausible rates -- there would be a wider crisis.
But the central cause is not the euro, even if it has meant Greece can't depreciate its own currency to ease the economic pain. Budget deficits and debt are the real problems; and these stem from all the welfare benefits (unemployment insurance, old-age assistance, health insurance) provided by modern governments.
Samuelson goes on to explain why this can be nearly impossible to fix.
The next few years will not be pretty.