Breichner noted that one of the ways the council has agreed to balance the budget and offset a higher tax increase is to eliminate a 2.5 percent cost-of-living raise for city employees for the coming fiscal year, which begins July 1.
The general fund supports departments such as police, fire and general administration.
Almost $800,000 of the $4.1 million health program would be covered by premiums paid by employees and retirees for their dependents. The rest of the insurance program would cover employees and retirees from the city's light, water and sewer departments, which are not in the general fund.
City Human Resources Director Don Francis said the health insurance plan will cost more because overall health care and prescriptions are becoming more expensive, plus the city exceeded its program deductible, which will prompt a higher rate next year.
Francis said 408 employees and 313 city retirees have health insurance plans with the city. City employees pay no premium for their insurance, but are charged 50 percent of the premium for dependents on their health plans.
As long as those with the city's coverage visit doctors within the program network, there is no payment for medical services except for $5 co-payments for doctor visits, Francis said.
Francis called it the "Cadillac" of health insurance plans.
Reducing cost would require changes to the health plan, but changes may be hard to pass.
The city's contracts with all four of its employee labor unions state that any changes to health insurance plans must be approved by the unions.
"In discussing this issue with our employees it's a matter of them helping us reduce costs," said Breichner. "At risk (this time) was their 2.5 percent pay increase."
"Something has to be done to control these costs. It doesn't help the employees to cause financial disaster for the city. ... Why cause a situation where the city has to lay people off? I don't think the employees want to see that," Breichner said.
The council meets at 7 p.m. at City Hall.