Mayor Mitch Landrieu said Tuesday that the city will face damaging budget cuts if New Orleans voters on Saturday again reject a proposition that would allow Sheriff Marlin Gusman to use an existing property tax to pay for court-ordered reforms at Orleans Parish Prison.

If the ballot measure passes, about half of the $8 million a year the tax now raises could be used in the first year to fund jail operations, and that amount would gradually increase over the 10-year life of the tax.

The measure’s failure, Landrieu warned, could jeopardize city dollars set aside for other critical services, including hiring new police officers.

“If this proposition does not pass, we are going to have to pay the money anyway,” Landrieu told reporters at City Hall, referring to the city’s obligation under state law to pay for OPP inmates’ care. “In order to do that, we are going to have to cut services that already exist in the city general fund.”

While Landrieu and Gusman have clashed over the mounting costs of implementing a consent decree the sheriff signed with the federal government, the two have found common ground in the property tax measure, a proposal rejected by 53 percent of voters in November. The proposition even has won the endorsement of the Bureau of Governmental Research, a nonpartisan research organization that has expressed repeated concern about the Orleans Parish Law Enforcement District, a taxing entity controlled entirely by Gusman.

Under existing law, the property tax, now levied at 2.8 mills, must be used to pay off bonds for criminal justice-related construction projects financed through the Law Enforcement District. As the bonds are gradually paid off, the tax is automatically reduced to cover only the remaining bonds.

“The problem is the law ties our hands about what we can do with that money,” Landrieu said.

The measure on Saturday’s ballot would allow Gusman to use proceeds from the tax that are no longer needed for debt service to pay for jail expenses, including the hiring of hundreds of new deputies. Therefore, the full 2.8 mills would continue to be collected. By the end of the 10 years, Gusman said, the tax would generate between $8.5 million and $9 million a year for jail operations.

“These funds are desperately needed,” Gusman said, “and they will not increase taxes.”

The sheriff, according to a recent BGR report, has estimated he’ll need $1.6 million a year to increase deputies’ salaries and an additional $4.3 million a year to hire 200 new deputies. The sheriff vowed to use the money “to make sure that we are running a constitutional jail, and that this facility is one that this community can be proud of.”

“Thanks to FEMA, we’ve been able to build the building that we need. Now we need to make sure that we have the funds to operate and maintain it,” Gusman said, referring to a new $145 million jail scheduled to open this year.

Further straining the city’s coffers is an $83 million contract Gusman recently awarded to an outside vendor, Correct Care Solutions, to provide medical and mental health care to inmates for five years, as mandated by the consent decree. City officials, appalled by the price tag of the deal, are disputing the validity of the contract in federal court.

“We do want to have a constitutionally run jail, and the way to do that is to fund the operations of the jail,” City Councilwoman Susan Guidry said. “As chair of the Criminal Justice Committee for the City Council ... I’m very, very familiar with what it’s costing to run our jail and with how much we need this measure to pass.”

Guidry was joined in endorsing the measure Tuesday by Councilmen Jared Brossett and James Gray.

Follow Jim Mustian on Twitter, @JimMustian.