How commissioners plan to fix Miami’s budget mess came into sharp focus Wednesday as the city announced agreements with three of its four unions just one day before the start of this month’s budget hearings.

The agreements, filled with givebacks like forgoing paid holidays and eliminating retiree healthcare payments, still must be voted on by union members before being ratified by the city’s five commissioners. That’s expected to happen by Monday, when the commission reconvenes.

Commissioners, who will hold public hearings Thursday and again Sept. 27, must send a balanced budget to Tallahassee before October.

Miami faces a $62 million deficit in 2012, caused mostly by overly optimistic revenue projections and the use of non-recurring fees to balance its books in 2011.

Wednesday, at a special pre-budget commission meeting, the public learned the lone stumbling block to balancing the city’s books is getting police to go along with a plan to cut $12 million from the department, mostly by eliminating pay supplements, three paid holidays, and special night shift pay from its 1,000 union members.

Another $5 million would be saved by not purchasing new police vehicles and by passing on the cost of physicals and new uniforms to employees.

The plan sparked anger from Fraternal Order of Police President Armando Aguilar.

“A lot of our officers are going to lose their homes. Where does it end? You’re going to be responsible for destroying this entire police department,” he said.

Commissioners peppered Aguilar over his refusal to give up a state tax that goes toward pensions, which the administration says would offset about two-thirds of the proposed pay cuts for cops. Aguilar said it required a unanimous vote by his union. City labor negotiators disagreed, saying it would be ratified by a simple majority when union members vote on a new contract.

Shortly before recessing, Commission Chair Wifredo “Willy” Gort told the two sides to “get together and try to come up with some solutions.”

Miami Mayor Tomas Regalado has proposed a $471 million operating budget with a slightly decreased tax rate of $7.57 for every $1,000 of taxable property. It means about a $30 savings for someone who owns a $300,000 home with a homestead exemption.

The mayor’s plan wouldn’t eliminate jobs or cut services, most of the savings would come from the backs of city workers, or from not filling hundreds of vacant positions citywide. Early on the mayor threatened the city’s unions by calling for almost a month of furloughs or massive layoffs. But the threat dissipated.

It’s the third year in a row Miami is cutting salaries to help balance its books. The city has seen its reserves plummet from more than $100 million only four years ago to $13 million today, as the city struggled to fill mounting pension payouts caused in large part by the declining stock market.

Still, in a city that has been besieged lately by bitterness and controversy, the news wasn’t all bad. Labor negotiators said they have come to terms with sanitation, general employees, and the fire union. The agreement with the fire union will save Miami $8.5 million, with most of it coming from a very similar pension account to the one causing the friction between police and the administration.

Fire — which was forced to give up a staggering $31 million last year when some firefighters lost more than 20 percent of their paychecks — also agreed to eliminate training during overtime, and not fill vacant positions, moves that will save the city almost $4 million.

The city will also save more than $2 million from its sanitation and general employees unions by forcing employees to take three furlough days.

The administration holds the aces as it negotiates with its unions this year. Like last year when Miami filled a $105 million deficit, the city has invoked a state statute called financial urgency that allows commissioners to unilaterally pare union contracts. Last year, commissioners cut more than $80 million from citywide union contracts.

Though the fire union continues to fight last year’s move in court, union President Robert Suarez said he felt it was wiser to work with commissioners this year rather than have them cut and choose from wherever they want.

“I don’t have to worry about their imaginations,” he said.