The governor, Alejandro García Padilla, and senior members of his staff said in an interview last week that they would probably seek significant concessions from as many as all of the island's creditors, which could include deferring some debt payments for as long as five years or extending the timetable for repayment.

"The debt is not payable," Mr. García Padilla said. "There is no other option. I would love to have an easier option. This is not politics, this is math."

It is a startling admission from the governor of an island of 3.6 million people, which has piled on more municipal bond debt per capita than any American state.

A broad restructuring by Puerto Rico sets the stage for an unprecedented test of the United States municipal bond market, which cities and states rely on to pay for their most basic needs, like road construction and public hospitals.