"I'm hopeful that we could have a positive resolution soon with regards, at least, to D.C. 47," Nutter said. "I'm not much of a betting man, but I remain hopefully optimistic."
D.C. 47, which represents about 4,000 social workers, accountants, and other white-collar employees, has not had a new contract since 2009, putting a strain on the union's health and welfare fund.
Wright said his members were facing a possible doubling of their contributions to pay for health care. He said he was "very pleased" with Nutter's decision to front the $2.5 million, which would be subtracted from any future contract.
"Basically, he asked and I said yes," the mayor said. "We want to make sure our public employees - folks over in D.C. 47 - have health care and their bills are getting paid."
Wright said contract talks, which are on hold through the holidays, have been "professional and respectful on both sides."
The city's larger, blue-collar union, District Council 33, also has been without a new contract since 2009, and relations with the Nutter administration have been difficult at best.
D.C. 33 president Pete Matthews has been an acid critic of Nutter's, and his members were a heavy presence at the City Council meeting in March when protesters drowned out the mayor's attempt to give his annual budget address.
Since then, Nutter has resolved another long-standing labor dispute - with the firefighters' union. That contract was settled shortly after a new union president, Joseph Schulle, was elected on a campaign promise to heal relations with the administration.
"Our longer-term goal is . . . to get all of our unions under multiyear, secure contracts with raises," Nutter said Thursday. "At the same time, as I've always said, it has to be a contract that respects the workforce and the hard work they do, but is also respectful to the taxpayers who have to pay for it."