Miami-Dade Mayor Carlos Gimenez proposed a stay-the-course budget Thursday for the next fiscal year that spares government services, funds programs for culture, seniors and children, and protects employees from layoffs.

Gimenez’s 2012-13 budget lowers the county’s overall property-tax rate by 2 percent, a reduction that could politically benefit him in his reelection bid next month. He campaigned a year ago on a promise to shrink the tax rate, which he and commissioners did last fall by nearly 12 percent.

And, on the most controversial sticking point, the mayor headed off another likely battle with unions by seeking to maintain a 4-percent employee healthcare contribution — but also setting money aside to cover the shortfall that would result should commissioners refuse to impose it.

Among the budget highlights:

• Restoring funds for the Miami Science Museum, the Miami Art Museum, HistoryMiami and the Vizcaya Museum and Gardens to 2006-07 levels;

• Refraining from propping up the general fund with millions borrowed from the Water and Sewer Department, as had been done in previous years, to save for anticipated costly repairs to the county’s antiquated system;

• Hiring the first two classes of police officers in three years, and recruiting new firefighters as needed to keep up with retirements.

“Our call volumes continue to increase, and we’ve been doing more and responding to more calls with less personnel for the past three or four years,” said Rowan Taylor, president of the Miami-Dade firefighters union, which has endorsed Gimenez, a former Miami fire chief. The department, unable to hire for several years, is short between 50 and 60 firefighters.

The spending plan is markedly different from the painful budget Gimenez put forth last year, two weeks after getting elected following the recall of Mayor Carlos Alvarez. Gimenez’s first budget laid out tough cuts and job losses, and relied on steep union concessions. In the end, the cuts were not as severe as initially feared.

Most unions hit an impasse over requiring employees to contribute the additional 4 percent of their base pay toward healthcare costs, for a total of 9 percent.

That concession, approved by a narrow, 7-6 majority of county commissioners earlier this year, is unlikely to pass muster again. Some commissioners are counting on union support in their own reelection races; one of them, Commissioner Barbara Jordan, swung the vote in favor of the concession but said she would not support it again.

Reading the political tea leaves, Gimenez’s budget sets aside $23 million to cover the cost of eliminating the additional 4-percent giveback from employees.

The proposal enables both the mayor and the commission to tally a win: The mayor gets to say he wanted a deeper tax-rate cut but did the responsible thing by budgeting for the commission’s likely refusal. Commissioners get to say they gave employees some of their pay back without going to another impasse.

If commissioners agree to continue the giveback, the mayor said, the $23 million pot could go toward improving services or further lowering the property-tax rate.

The 4 percent “was a tough sell last year, getting it through the commission,” Gimenez acknowledged in an interview.

Commissioners will meet Tuesday to set the preliminary tax rate. They will be able to lower but not raise it when they vote on the budget after two public hearings in September.