A higher minimum wage raises peoples' incomes at a greater rate than it'd increase prices in affected industries.
You're establishing a wage floor. Income will rise for most workers. Some will lose their jobs, increasing the strain on the public welfare/unemployment entitlements. You're proliferating the current perverse system that pays people not to work, rather than paying them a subsidy to continue producing.
The entitlement paradigm is given a blanket endorsement under the false pretense that increasing wages will create greater aggregate demand in the economy, which will lead to hiring in other industries. It hasn't happened since the Oil Crisis and the rise of Japan. Instead, jobs are outsourced, and middle class income leaves the country as import spending rises.
How many more decades will this continue before the left-wing Keynesian rabble-rousers come to their senses?
Cost of labor to producers must go down. The Bush administration used deficit spending to put downward pressure on the dollar and export our price inflation to countries who buy dollars. Our ability to continue that arrangement has been severely impaired by the Great Recession. What do you want to do now? Suck harder on the Great Soceity status quo?