Those leaders - Herman J. "Pete" Matthews of AFSCME District Council 33 and Catherine G. Scott of District Council 47 - say Nutter reneged on a promise to give their members a fair contract, a commitment he made in 2009 to get their support for a sales-tax hike and a delay in city pension contributions during the depths of the national recession.
Without new agreements, the workers' wages and benefits have been frozen since mid-2009.
Over union protests and a pending lawsuit, the administration has suspended yearly step raises for employees in their first five years on the payroll, along with smaller longevity increases, paid to veteran workers for every five years' service.
Nonuniformed city workers staff every department, with duties that include collecting trash, writing prescriptions, inspecting buildings, and monitoring water quality.
Police and firefighters negotiate separately, their contracts usually settled by arbitration.
But only the police have a settled, five-year contract, running through 2014. An arbitration award giving firefighters a series of 3 percent raises over three years was thrown out by a judge last year because it did not give adequate weight to the city's financial situation. That dispute is back in arbitration.
D.C. 33 took the offensive last week with radio and cable TV ads, including a 2008 video clip of Nutter at a union meeting promising he would "make sure that you have decent wages, good health care, and a fair and reasonable contract."
"The mayor," the ad says, "has not kept his word."
Nutter fired back in an interview with WHYY's Dave Davies, noting that unlike many other cities, Philadelphia has avoided major layoffs during the recession.
"Our public employees deserve a fair contract that is also fair to the taxpayers of this city," Nutter said.
"We're still in the aftermath of the worst recession since the Great Depression, we have a pension fund that is only 50 percent funded, we've had to make significant reductions in services, and we've had to raise taxes to maintain those services," he said. "I'm not willing to kick the can down the road and just make a deal for the sake of having a deal."
Neither side appears eager or willing to escalate the stakes with a work stoppage.
Nutter could declare an impasse and impose the city's last, best offer on a take-it-or-leave-it basis. The unions could strike, but their leaders suggest it would be a mistake.
"I do not want my people to go out on strike," said Matthews, president of D.C. 33 since 1996. "I think it would be detrimental to them, it would be detrimental to the public. . . . [The mayor] would keep us out there as long as possible, and then we would have to come back and take anything he wants. . . ."
So the deadlock continues.
Every few months, a delegation of city officials meets with a delegation of union leaders, laying out its most recent proposals. The unions may take days or weeks to deliver a formal response, but the gist is apparent on the spot: No way.
Meeting with D.C. 33 on Thursday, the city reduced its demand for the right to furlough employees from 20 days a year to 15 - the equivalent of a 6 percent pay cut, the unions say. Scott, head of D.C. 47, said Nutter would not ask for furlough authority unless he intended to use it.
Despite escalating health-care costs, city payments to the unions' health and welfare funds haven't risen since mid-2008 - $975 per member per month. The unions have rejiggered their plans repeatedly trying to cover expenses.
Since Nutter took office, his five-year budget projections have assumed employee costs would remain essentially flat regardless of inflation.
In effect, that means any basic wage increases would have to be offset by savings - reduced overtime, for instance, or use of furloughs to pare expenses.
The city's most recent salary offer for nonuniformed workers was a 2.5 percent across-the-board raise effective Jan. 1. There would be no additional compensation for the previous 2.5 years.
Scott said the offer did not account for concessions on furloughs, pension contributions, or overtime. "When they come in and they say, 'We're making a wage offer of 2.5 percent, but on the other side we want you to give up 16 or 18 percent,' that's not a serious negotiation," she said.
Scott also said the administration had not explored various union recommendations, like reducing the use of outside contractors or trying to secure payments in lieu of taxes from nonprofits.
The city's five-year plan already projects $12 million in annual benefits savings from new contracts with AFSCME and firefighters. The city's best hope for those savings is a self-insurance model, already in effect for nonunionized and police personnel. That model is credited with reducing health payments $13 million last budget year.
Instead of paying premiums to an insurance company to cover all medical expenses, the city agrees to pick up the expenses and pays the insurance firm a much smaller amount, to negotiate charges with medical providers and process claims.
D.C. 33 has already gone to a self-insurance model with its own health and welfare fund, and D.C. 47 supports the concept, Scott said. But the city has been unwilling to help D.C. 47 with the millions of dollars in escrow that Independence Blue Cross requires to move to self-insurance, Scott said.
The current pay freeze meets Nutter's goal of holding labor costs steady, but without any progress on the city's biggest fiscal problem - the $4.7 billion hole in the city retirement fund, the cumulative result of mayors and City Councils underfunding pensions for the last 50 years.
The administration wants current employees to contribute more toward their pensions - 3.6 percent of salary instead of 2.2 percent.
Scott said the required contribution would climb to nearly 10 percent for some current workers.
Future workers would be forced into a hybrid pension plan, with defined benefits no higher than one-quarter of an employee's final average salary. On top of that, the employee would make payments into an investment plan like a 401(k), and the city would provide a partial match, up to 1 percent of a worker's salary.
Contact Bob Warner at 215-854-5885 or email@example.com.