Its economy has been mired in recession for years. The public is fed up with austerity. Investors want big premiums to lend to a government deep in debt, with no ability to devalue its currency.

Greece? Try Puerto Rico, the U.S. commonwealth whose long-simmering debt crisis—its $72 billion debt equals nearly 70% of its economic output, far more than any U.S. state—is about to come to a boil.

The...