One is to defend the euro at all costs. The immediate consequences for Greece — or other countries — of leaving the euro would be dire. Some companies, unable to repay euro-denominated debts, would go bankrupt. Inflation would shoot up. Banks might suffer large withdrawals. Worse, if Greece dropped the euro, it might trigger a chain reaction. Depositors in Spain, Italy or Ireland might stage runs on their banks, trying to withdraw euros before they were replaced by less valuable national currencies.

Preserving the single currency could cost trillions of euros, says Douglas Elliott of the Brookings Institution. The ECB might have to guarantee bank deposits or provide vast advances to banks to offset withdrawals. Softening today’s austerity would require more borrowing. Who would lend? The ECB? Historically, excessive lending by central banks risks high inflation, though many economists discount that now. What about “eurobonds” — bonds issued for individual nations but backed by all? This would make Germany, with its strong credit rating, the ultimate guarantor. Naturally, the Germans resist.

The other possibility is to admit that defending the euro is self-defeating, argues economist Desmond Lachman of the American Enterprise Institute. Imposing big spending cuts and tax increases on economies in recession worsens the recessions. Spain is supposed to cut its deficit by more than 3 percent of its economy in 2012, even though retail sales are down 11 percent from year-earlier levels. Budget targets won’t be met, he says. The only hope for these countries is to jettison the euro and benefit from a cheaper currency.