The study from The Pew Charitable Trusts found that the New Jersey and Kentucky public pension funds are in such perilous shape that they risk running dry.

"Even after eight years of economic recovery — eight straight years of stock market gains — the public pension plans are more vulnerable than they've ever been to the next recession," researcher Greg Mennis said in an interview.

Governments have been ramping up contributions to the funds to help cover the promises they've made to retirees, but that leaves less money to spend on schools, police, parks and other core government services.

Another option is reducing pension benefits. A plan to do that in Kentucky led to teacher walkouts earlier this year.

The Pew study, published by the Mossavar-Rahmani Center for Business and Government at Harvard University, examines what would happen to pension funds in 10 states under various economic scenarios.