For the second time in two months, New Orleans officials on Tuesday found themselves trying to persuade a judge not to hold them in contempt for failing to pay millions of dollars the court has ruled the city owes to its firefighters.

And once again, they’ve been given an ultimatum: Resolve the situation or, as Civil District Court Judge Robin Giarrusso put it, “I’m going to have to take some steps I don’t want to take.”

The scene that played out in Giarrusso’s court Tuesday was almost a rerun of the arguments the two sides made over the summer in a case in which Civil District Court Judge Kern Reese ultimately ordered that Mayor Mitch Landrieu be placed under house arrest. Reese’s ruling was stayed at the last minute by the state Supreme Court.

Giarrusso put off deciding whether to follow a similar path, saying she wanted to give the high court time to weigh in on the question of whether the courts can force city officials to pay millions of dollars they don’t want to.

After saying she would wait until January for that ruling and then take her cues from the Supreme Court, she suggested she was already thinking about taking further steps in the case.

“I have ideas that are a little bit different than Judge Reese does,” Giarrusso said.

Giarrusso and Reese oversee two separate cases linked by the fact that both involve judgments against the city worth tens of millions of dollars to the firefighters and their pension fund and by the fact that despite those rulings the city has not paid at least some of the money.

The case in Giarrusso’s court involves the Landrieu administration’s failure to pay into the pension fund, which led to a judgment that the city owes $31 million in overdue payments and must pay the proper amount in the future. The administration paid about $4.6 million toward that judgment last year and has spread another $5 million in payments over the course of this year. The pension fund’s board has been pushing for the balance.

The case before Reese involves about $75 million the city owes firefighters in back pay for state-mandated raises the city refused for many years to implement. In that lawsuit, which stretches back decades, firefighters also are seeking about $67 million in interest and tens of millions in other payments.

City officials have attempted to link the cases. Andy Kopplin, Landrieu’s chief administrative officer, said in court Tuesday that the city has no plans to pay the pension fund money while it continues efforts to negotiate a global settlement with the firefighters covering both cases. The city and firefighters have been in mediation in an attempt to reach such a deal for months.

Giarrusso said she was “extremely troubled” by the lack of a plan.

“I told you the last time you were here I was going to give you a lot of rope,” she said. “I hope you didn’t all hang yourselves with it.”

The city’s legal argument is that while courts can order it to pay, they cannot actually enforce that order by holding the city in contempt, seizing assets or punishing officials because doing so would violate the state constitution and infringe on the separation of powers.

The city also has argued that because its annual contributions to the pension system are calculated based on how much is needed to increase its funding level, it doesn’t matter whether the judgment is paid immediately or over time.

In March 2013, Giarrusso ordered the city to “immediately” pay $17.5 million to cover the city’s 2012 obligations to the pension fund. She issued what she called a “peremptory writ of mandamus” ordering the city to pay that amount, plus interest, as the city’s “actuarially required contribution” for 2012.

Although state courts normally cannot compel political jurisdictions to pay legal judgments, Giarrusso’s ruling indicated she believed the city could be compelled to comply with a legislative mandate to pay whatever sum was required each year to fund the system.

Councilwoman Stacy Head, who chairs the council’s Budget Committee, and Kopplin also argued Tuesday that the city doesn’t have the ability to pay either judgment immediately, in light of tens of millions of dollars in spending required by the federal consent decrees covering Orleans Parish Prison and the New Orleans Police Department and the roughly $35 million in other unpaid judgments the city faces that stretch back to the 1990s.

Firefighters have argued the city could dip into reserve funds, the BP settlement or other sources immediately or else pay the money over a relatively short time frame.

When asked on the stand whether she would vote for a measure appropriating the funds if it was requested by the administration, Head said she wouldn’t.

“I don’t believe we have the ability to do that, so no,” Head said, adding that appropriating that amount of money would be “disastrous” to the rest of the city’s budget.

Follow Jeff Adelson on Twitter, @jadelson.