“We can’t figure out where is the end of this surplus account. What is it being built up for?” Terry Murphy, a public affairs consultant working for the unions, told the Miami Herald’s editorial board Monday.

The county has already declared an impasse over the concession provisions — excluding the healthcare contribution, which is still pending — with five unions. A sixth, representing solid waste workers, is at impasse over both the healthcare contribution and the other concessions.

“I expect this to get very political,” Gimenez said.

The mayor’s proposal to fund the $19 million no-kill animal shelter plan will likely face pushback from some commissioners who have questioned whether the county should pursue the tax-rate hike while the economy is still sluggish.

Commissioner Esteban “Steve” Bovo suggested from the dais last month that some voters might not have supported the animal shelter ballot measure had it been binding. “They felt, ‘Well, it’s not going to raise my taxes — it’s only a straw-ballot question,’ ” he said.

Commissioners will meet next Tuesday to set the maximum tax rate, which they can lower but not raise later. They will vote on the budget after two public hearings in September.

The higher tax rate would be the first pushed by Gimenez, who took the reins after a frustrated electorate ousted former Mayor Carlos Alvarez in a recall prompted by Alvarez’s unpopular 12.4 percent tax-rate hike and employee pay raises in 2010.

In the budget he delivered in 2011 after taking office to complete Alvarez’s term, Gimenez reversed his predecessor’s handiwork and called for severe services cuts, layoffs and dramatic employee concessions. Last year, a month before his reelection bid for a full four-year term, Gimenez proposed further reducing the tax rate, while maintaining services and avoiding job losses.

For the fiscal year that begins Oct. 1, the overall budget would total $6.4 billion, up from more than $5.9 billion last year. That includes $1.9 billion for construction spending, up from $1.6 billion last year to pay for big-ticket projects such as upgrading sewer pipes as mandated by the federal government, rehabilitating the West and Bear Cut bridges on the Rickenbacker Causeway and dredging Port Miami.

The operating budget for day-to-day expenses, including salaries and services, amounts to $4.4 billion, higher than last year’s $4.3 billion.

No layoffs are proposed in the budget. Despite the frozen vacancies and the elimination of 219 positions, the county’s workforce would grow by 206 positions to 26,109 because some port security and parks maintenance jobs slated to be outsourced will be kept in-house.

The office of human rights and fair employment practices would merge with the human resources division — currently under the county’s internal services department — to create the new department of human resources.

The budget calls for several fee and rate hikes, chief among them an 8 percent increase to water rates already approved by commissioners. Additional 6 percent increases are projected for the following two years, and 5 percent increases for the two years after that.

Public transit fares are also slated to increase to $2.25 from $2, following a commission-approved measure to tie ticket prices to the consumer-price index. Admission fees at Vizcaya Museum and Gardens would rise to $18 from $15.

Like last year, the budget plans for new classes of police officers (four) and firefighters (one) to make up for those who retire or leave the department. An additional 27 sworn police officers could be hired if the county receives a federal grant.

The budget also continues to boost funding for maintenance and programming at county museums and arts venues, including for the Miami Science Museum scheduled to open next year.