Fudge spoke in favor of raising the wage at an event in Cleveland with liberal political organizing group ProgressOhio.
Fudge told ideastream afterward she thinks she can get enough Republicans to vote for a raise if they come under pressure from their home district voters.
"There are people in both parties who are making less than the minimum wage and who are struggling every day," Fudge said. "So they need to let their voices be heard. They can't sit back and be silent. They need to put the pressure on their representatives on both sides of the aisle."
Fudge said she would need 20 Republicans to back a minimum wage increase for it to pass.
"And I guarantee you there are more than 20 Republicans whose districts want to have a raise," she said.
Ohio's minimum wage is now $7.95 an hour for businesses making more than $292,000 -- 70 cents higher than the federal minimum wage. President Obama this year signed an executive order setting a minimum $10.10 hourly pay for federal contractors.
House Speaker John Boehner has opposed increasing the minimum wage, calling it "bad policy" in a press conference in January.
