Metzner said he expects council members will suggest relatively smaller items to cut from the budget.
Any cuts could be used to offset part of the proposed tax increases.
The council could lessen the proposed tax increases by finding ways to bring in additional money, such as rate and fee increases, or levying a new city charge.
The council asked Zimmerman to look for ways to bring additional money into the city, and present his findings next Tuesday.
The proposed tax increases would help balance the proposed $25.7 million general fund, which pays for city departments, including police, fire and public works. The proposed general fund calls for an almost $1.2 million increase in spending on city employees' wages and benefits, including a 2.5 percent cost of living raise, plus about $500,000 in increased spending on vehicles and construction projects.
The proposed tax increase would cost a Hagerstown homeowner with property assessed at $100,000 an additional $53 next year. That homeowner's city real estate tax bill, $732 this year, would be $785 next year.
A business with equipment assessed at $10,000 would pay an additional $13 next year if the proposed tax increases are approved. That business' equipment tax bill from the city, which is $183 this year, would be $196 next year.
The business equipment tax is determined by the cost, minus depreciation, of business equipment such as furniture and computers. Manufacturing equipment and inventory items are exempt from this tax.
The general fund is the only city fund that receives money from city taxes. City funds such as the water and sewer funds depend on income from water and sewer bills.
The proposed budget also calls for the water and sewer rates each to increase 3.5 percent.
Councilman Kristin B. Aleshire said Tuesday the council should increase those rates more for water and sewer customers outside city limits, and lessen the rate increases for city residents.
A public hearing on the proposed budget is scheduled for 7 p.m. April 30.
The council is scheduled to approve a new budget on May 28.