CHICAGO — Corporations are moving in, and housing prices are looking better across the region. There has been a slight uptick in population. But a crushing problem lurks beneath the signs of economic recovery in Chicago: one of the most poorly funded pension systems among the nation’s major cities. Its plight threatens to upend the finances of President Obama’s hometown, now run by his former chief of staff, Rahm Emanuel.

The pension fund for retired Chicago teachers stands at risk of collapse. The city’s four funds for other retired city workers are short by $19.5 billion. At least one of the funds is in peril of running out of money in less than a decade. And starting in 2015, the city will be required by the state to make far larger contributions to the funds, which could leave it hundreds of millions of dollars in the red — as much as it would cost to pay 4,300 police officers to patrol the streets for a year.

“This is kind of the dark cloud that’s coming ever closer,” Mr. Emanuel said in a recent interview, adding that he had no intention of raising his city’s property taxes by as much as 150 percent — the price tag, he says, that it might take to pay such bills. “That’s unacceptable.”

Illinois lawmakers, who make key financing and benefit choices for Chicago’s pension system, have wrestled for months without agreement on the politically troublesome matter of cutting the benefits of public sector retirees to save money. And last month, Moody’s Investors Service downgraded Chicago’s rating by an unexpected three notches as part of a broad reassessment of how pensions are affecting the financial strength of cities. That “super downgrade,” in the parlance of the bond market, left Chicago, the nation’s third-largest city, with a lower rating than 90 percent of Moody’s public finance ratings.