The upcoming budget for Miami-Dade County has become a political chess match between Mayor Carlos Gimenez and Commission Chairman Joe Martinez, his chief rival in the upcoming mayoral election.

The key pieces sure to be manipulated: controversial employee healthcare contributions imposed on unionized employees, and the county’s property-tax rate.

Gimenez says his reorganization of county government, which slashed the number of departments to 25 from 42, will result in $40 million in savings for the next fiscal year. That, coupled with a projected rise in the county’s property values, means there could be wiggle room for the mayor, chairman and commissioners to make some politically popular moves — right before most of their names go on the ballot this fall.

Martinez told Gimenez in a memo two weeks ago that, if the county finds itself with more money, he would like to reduce the property-tax rate, restore services or lower the healthcare contribution. The chairman reminded the mayor that the commission ultimately controls the county’s approximately $6 billion purse strings.

Gimenez countered last week with a memo of his own, saying his budget will propose shrinking the healthcare contribution and possibly lowering the property-tax rate.

Even though the ideas coming from the two men favored to get to a November runoff after August’s mayoral election are virtually identical, getting credit this election year is tricky.

That’s because, though the mayor proposes the county budget in July, Martinez has enormous sway over the commission and can make changes to it up until the end of September. And sandwiched in between is the primary election, with the expected runoff between the two in November after the budget is due.

The county already lowered the property-tax rate last year, following the recall of Mayor Carlos Alvarez, who was targeted in part for hiking the rate the year before. Both Gimenez and Martinez can — and do — take credit for residents’ slightly smaller property-tax bills.

Now they’re vying for support from labor unions, which typically offer valuable hands-on volunteers, organization and campaign contributions to their preferred mayoral candidate.

Gimenez won a hard-fought campaign last year even though most unions backed former Hialeah Mayor Julio Robaina, his opponent. This time around, Gimenez may be even more unpopular with labor, as the mayor who asked the county’s 13 commissioners to require employees to contribute an additional 4 percent of their base pay toward healthcare, bringing their total contribution to 9 percent.

Martinez was one of six commissioners who voted against imposing the concession, which applied only for a year.

Gimenez’s administration is grappling with how to tackle expensive healthcare costs for next year while placing less of a burden on the county’s nearly 26,000 employees. Administrators have begun a new round of intense talks with eight of its 10 employee bargaining units to try to cement a new, three-year healthcare plan. All 10 unions agreed to substantial cutbacks this year to close a big budget gap.

Most of the scenarios the administration has proposed involve lowering or eliminating the added 4-percent employee contribution. But they also call for higher co-pays and more expensive healthcare coverage for dependents such as spouses and children.