That relationship has been finding its footing. Mr. Orr recently disavowed a letter on labor contracts sent out by the mayor’s office without his permission. On Friday, after Mr. Bing met with the Council, the emergency manager released an order that gave them approval to conduct city business, though he retains the last word on their decisions.

Next week, the Council is expected to vote on a contract to hire Mr. Orr’s former law firm, Jones Day, to help with the city’s restructuring. The deal raises concerns about a possible conflict of interest. Mr. Orr, who said he was not involved in the selection process, said he would probably approve the contract regardless of what the Council decided. He has allowed the public discussion for the sake of transparency, he said, a function council members are quick to cite when asked about their future role.

Such courtesies may soon get in the way of the swift, unpopular decisions Mr. Orr is expected to make, as many expect the meet-and-greet phase of his tenure to quickly come to a close.

“I’m trying to err on the side of fairness and balance, perhaps to my detriment,” Mr. Orr said in an interview this week. “At some point, my desire to do this the right way and be fair is just not going to work anymore.”

Mr. Orr, who has not yet met with union leaders or creditors, is required to submit a restructuring plan to the state treasurer in early May. Major changes to the City Council may be coming.

In his budget on Friday, Mr. Bing proposed a reduction in the Council’s $11 million budget, shrinking each member’s staff to only one person. The $4 million in savings is less than the $7 million cut recommended in a recent report by a consulting firm hired by the city, which suggested that the Council become a part-time body.

Council members now have four to eight staff members. They say one person would not be enough to serve constituents and review complex city contracts, though Mr. Orr will make the final call on funding.

“His sweet spot is dealing with creditors,” Gary Brown, the Council’s president pro tempore, said of Mr. Orr. “Everybody else believes he’s going to get mired down into the weeds of trying to run city government. That would be a mistake.”