Public sector union leaders have been enraged by Mr. Emanuel, who was at the helm in 2012 during this city's first teachers' strike in 25 years and who has announced plans to phase out city health care coverage by 2017 for some city retirees. A change in pension benefits could affect more than 70,000 people who worked as Chicago police officers, teachers, firefighters and others, and who now receive average annual benefits ranging from about $34,000 for a general-services retiree to $78,000 for a former teacher with 30 years of service.
Some labor leaders say the city, not the state, is ultimately responsible, arguing that Chicago leaders long ago should have begun planning how to pay for pensions promised to its workers, regardless of insufficient state contribution formulas.
"The city failed to fund this all along, and now Mayor Emanuel has made it clear he is going after the hard-working men and women on the Chicago Police Department to make up for that," said Michael K. Shields, president of the Fraternal Order of Police, who described Mr. Emanuel, simply, as anti-labor. "He's trying to stiff us out of our pay."
(Read more: If Detroit cuts pensions, will your city be next?)
All sorts of political battles are emerging from the pension crisis. Candidates from both parties are seeking Mr. Quinn's job next year, many of them citing the state's inability to untangle the pension woes as reason to toss out those holding office. William M. Daley, another former chief of staff for President Obama and now a Democratic candidate for governor, said in an interview, "Anyone who thinks that this is just a problem on paper, those are the same people who looked at Detroit 20 years ago and said, 'Don't worry about it, we can handle it.' "
Mr. Emanuel has made clear his plans to seek a second term as mayor in 2015, and no major challenger has emerged so far. But the city's looming pension debt — and the bills that will balloon by election year — may carry political fallout from unions as well as ordinary Chicagoans.
"Voters don't care about pensions as an abstract issue," said Dick Simpson, a former Chicago alderman and political scientist. "What they care about are the effects over the next two years of having to cut services or raise taxes to pay for this."
Over all, experts say Chicago's financial health has improved since the recession; city revenues are growing again and the population, which fell during the decade after 2000, has grown modestly since 2010. The city's general budget fund faces a potential shortfall of $339 million in 2014, but city officials say that gap is lower than initially expected and manageable.
Circumstances grow far more complicated a year later, when state law will require Chicago to pay significantly more — $1 billion a year — into the city's pension funds, to make up for years of underpayments. Even sooner, the Chicago Public Schools, which draws from the same tax base, is required to find an extra $338 million for its pension fund, and more every year after that.
Unless the legislature agrees to a complete overhaul of the pension plans, Mr. Emanuel said, he will not even entertain the notion of raising Chicagoans' taxes.
"What the system needs is a hard, cold dose of honesty," Mr. Emanuel said. "I understand the anger. I totally respect it. You have every right to be angry because there were contracts voted on."
He added: "People agreed to something. But things get updated all the time."
—By Monica Davey and Mary Williams Walsh of The New York Times