The bulk of the budget is $4.3 billion for day-to-day expenses, including salaries and services, compared to nearly $4.5 billion last year.

That portion of the budget covers increased funding for the museums, whose county dollars were cut between 25 and 30 percent since 2006, said Roxanne Cappello, interim president/CEO and CFO of HistoryMiami.

“I’m very happy,” she said. “This gives us a little bit of a breather. We can add a little more to our exhibitions. We can continue to add curriculum to the programs that we deliver to the school system.”

Unlike in years past, the county will not be propping up its general fund with money transfers from the water and sewer department, which is expected to be on the hook soon for a multibillion-dollar plan being negotiated with federal regulators to upgrade Miami-Dade’s system. The department loaned $25 million to the general fund last year, which the general fund will begin paying back next year.

The budget also delegates the federally funded Head Start program for pre-K children to private providers and the public school system. The county, which administers the federal funds for the program, had been running Head Start using a mix of private providers and county facilities run by county employees.

Gimenez said the school district is trying to hire those employees as teachers. They won’t get paid the same as in the county, he said, but the program could be expanded to 500 more children with the same federal funding because it will be cheaper to run.Commissioners, who received the thick budget books Thursday afternoon, were digesting the mayor’s proposal.

Commissioner Xavier Suarez, who voted against the 4-percent healthcare giveback, said he had hoped Gimenez would eliminate the concession himself. But Suarez was glad to hear money had been set aside for commissioners to do away with the contribution.

“We have a good start here,” he said.