Puerto Rico is fighting to stay afloat in a rising sea of debt.

Its economy is sputtering. Its population is shrinking. Its recent election is disputed. Its public pension fund is perilously low on cash. The U.S. territory has just been through a brutal five-year recession, something not experienced in the United States as a whole since the 1930s.

Desperate to raise cash, Puerto Rican officials have been selling off anything they can: two toll roads and the main airport so far.

To bring in tax revenue, they are trying to lure people out of the underground economy. Coffee shops, hairdressers, even outdoor market stalls are being required to issue printed receipts with every sale. The receipts carry a lottery number, with a chance to win cars or cash, as an incentive to get shoppers to pay the island’s 7 percent sales tax.

Though many of Puerto Rico’s problems are reminiscent of Greece’s — tax noncompliance, a stagnant economy, years of issuing long-term debt to cover short-term payments — investors have had a nearly insatiable appetite for its bonds.

But now their support is dwindling. Some big investors are pruning their holdings. That is beginning to widen the cost of borrowing for Puerto Rico relative to other states and municipalities, which are benefiting from a big decline in borrowing costs. The interest rate its 30-year bonds now pay is about 2.5 percentage points higher than other municipal borrowers’, up from a difference of just 1.5 percentage points at the beginning of 2012, according to Municipal Market Data.

The possibility of a credit downgrade also hangs in the air, something that could lead to more selling.

“There is no specific event looming on the horizon,” said Alan Schankel, a managing director at Janney Capital Markets in Philadelphia. “But it’s a problem of immense magnitude, and it’s very challenging to sit here and see how they work their way out of it.”

Puerto Rico needs to be able to issue bonds at attractive rates to cover its short-term financing needs. Perhaps more important, it has to figure out how to salvage its retirement funds. After shortchanging them for years, it now has the weakest major public pension system in America.

The main fund, which serves about 250,000 government workers, past and present, is only 6 percent funded — a small percentage of what is considered the minimum needed for a marginally healthy pension plan — and could run out of money as soon as 2014. Another fund, for about 80,000 teachers, which is 20 percent funded, will last just a few years longer if nothing is done. Police officers and teachers in Puerto Rico have opted out of Social Security and rely entirely on their pensions.

“For now, I’m not totally shaken about the possibility of the fund going broke,” said Jorge Ramon Roman, a 78-year-old retired instructor for the island’s Civil Air Patrol. “But I do fear for the future, when I’ll be an even older person, more infirm and with less of a pension.”

Hector M. Mayol Kauffman, the executive director of the pension system, said it would be impossible to cut the benefits of people who are already retired, citing court precedent.

Puerto Rican officials were racing this fall to put together a rescue plan for the pension fund. Voters, though, pushed out Gov. Luis Fortuno, who had tried austerity measures that included cutting tens of thousands of government workers along with a revamping of the fund.

They elected Alejandro Garcia Padilla, who promised to create 50,000 jobs in the next 18 months. But the margin was razor-thin and Fortuno has requested a recount.

Since the election, yields on the island’s 30-year bonds have continued to widen.

In addition to selling assets and restructuring bonds to postpone payments due, officials have also been pitching Puerto Rico as a hot new tax haven for hedge funds, real estate investors and other high-paying businesses, hoping to attract jobs and spur growth.

That strategy has worked in the past, attracting a number of big pharmaceutical companies — but last year Fortuno’s government hit those companies with a big excise tax, to help pay for tax cuts for nearly everyone else. There are hopes that the U.S. Treasury will grant the affected companies a separate tax break.

Outstanding public debt has exploded to about $67 billion, although tallies differ depending on what types of debt are counted. Relative to personal income, Puerto Rico’s public debt is almost 10 times that of Hawaii, which has the highest debt-to-income ratio of the 50 states, according to Moody’s Investors Service.

Puerto Rico does not have the extra $2 billion a year it would need to pay its retirees if it exhausts its retirement fund. A collapse of the fund would set off a broader fiscal emergency, with officials forced to make excruciating choices among paying schoolteachers and the police, fixing the roads, providing drinking water and paying all those far-flung bondholders on time.