The increase would bring in an additional $131,580 a year and help balance the $21.6 million general fund budget, which in January was projected to have a $1.1 million deficit.
"People in elected office have to be willing to raise taxes if they have to," Breichner said.
He said residential property taxes are tax deductible expenses, while trash collection fees are not.
The property tax rate is $1.74 per $100 of assessed property value, and would remain the same under the proposed budget. A penny of the property tax is worth about $70,000 in revenue, City Finance Director Al Martin said.
At least two council members favor the proposed rate increase.
Councilmen Alfred W. Boyer and J. Wallace McClure said the rate increase will bring the trash collection revenue closer to expenses.
The service costs the city about $411,000 a year. With the proposed rate increases and cuts in service - including cutting trash collection from twice to once a week - trash collection and disposal will cost the city about $95,000.
Breichner said the service was never intended to break even. The fee was only supposed to cover the cost of disposing of the trash in the Washington County landfill, which it does, according to the proposed budget.
Metzner favors either eliminating the trash collection fee and increasing property taxes to pay for the service or making trash a self-sufficient service, which he expected would translate into an higher rate increase and a property tax cut.
About 13,140 households use the city's trash collection service. Metzner said if the trash collection fee is eliminated, the city should bring the service to as many of the estimated 3,500 households without the city service as is possible.
"I think there's a lot to be discussed," Metzner said. "I'm not happy with the thought process behind raising the trash collection fee if this is a method to balance the budget. I don't like revenue enhancers."
Councilwoman Susan Saum-Wicklein could not be reached for comment.
A public hearing on the budget is scheduled for May 4. The council is expected to vote on adopting the budget May 25.