Illinois used to have a plan to pay off the gaping shortfall in the pension funds that pay retired teachers, university employees, state workers, judges and politicians, Dan Long recalls.

Mr Long, director of the Commission on Government Forecasting and Accountability, the non-partisan auditing arm of the Illinois state legislature, remembers that, back in 1994, the state laid out a proposal that would have paid off most of what was then a $17bn gap by 2011.  But Illinois could not stick to the plan.

With financial year 2011 less than six weeks away, the pension arrears of the 1990s look quaint. Instead of a balanced system, the state faces unfunded liabilities of about $78bn, the biggest pension hole in the US, and contributions of more than $4bn for 2011, the largest single element of its $13bn budget deficit.

Illinois is the poster child of unfunded pensions in the US. But state retirement systems could become a national concern, new research shows.

Joshua Rauh, associate professor of finance at the Kellogg School of Management at Northwestern University said that, without reform, some state pensions might run out within the decade. By 2030, as many as 31 states may not have the money to pay pensions. And, if these funds exhaust their assets, the size of payments for the benefits they have promised will be too large to cover through taxes, putting pressure on the federal government for a bail-out that could potentially cost more than $1,000bn, he says.

“It is more than a local problem,” Mr Rauh said. “The federal government could be on the hook.”

Estimates put the unfunded liabilities at between $1,000bn and $3,000bn after years of states promising benefits but not contributing enough in both good times and bad to cover them.

Many states base their calculations on an 8 per cent annual return and use an accounting method called smoothing, which staggers gains and losses over several years, two factors that some observers warn could mask the size of the shortfalls. The problem has come to the fore with the financial crisis and recession. Pension funds, like most money managers, suffered losses. The tax revenues that fund annual contributions to pensions, along with essential services such as healthcare and education, have plummeted, leaving little room to reimburse the losses.

States have begun reforms, with some lowering return expectations and raising employee contributions and retirement ages.

Mr Rauh said subsidising pension borrowing would cost a net $75bn with new contributions to the national Social Security programme offsetting some of the subsidies.

By his calculations, which assume the 8 per cent return, Illinois would run out by 2018 followed by Connecticut, New Jersey and Indiana in 2019. Some 20 states will have run out by 2025.

Five states would never run out, including New York and Florida, and 17 other states have a horizon of 2030 or beyond.

“We had to make cuts: education, healthcare, local government support and not-for-profit providers,” Mr Megna said of the last year’s budget process.

New York’s governor has proposed borrowing from the pension system, which is about 94 per cent funded, as the state did after the September 11 attacks, and repaying it with interest if low tax collections persist, Mr Megna said.

For fiscal 2010, Illinois sold $3.5bn of bonds to pay for its annual contribution.

But in an election year, there is no political support in Springfield, the capital of Illinois, for another bond issue, particularly since it requires a two-thirds majority in the state legislature.

The most likely outcome is that the state will defer the issue to next year. “That’ll have an impact in terms of lost investment opportunities, and they’ll have to sell some of the portfolio to pay the pensions,” said Mr Long.