The notion that higher minimum wage discourages hiring is entirely unproven. In plenty of places, employment is up in the years after an increase. In general, a few years later, you cannot see any difference.
This notion is a conservative canard without merit. There are two huge flaws in addition to the superficial inaccuracy. First is the notion that employment at the current minimum wage is something that should be encouraged. Spending forty, fifty or sixty hours a week at an activity that does not provide enough money to support even one person, let alone a family, is a bad thing for everyone except the employer, both society and the worker are worse off.
The worker is deprived of almost everything that people claim to believe makes us human. Time with family, opportunity to learn, fun, self-improvement, child and elder care, exercise, you name it never happens. Add food insecurity, no preventative health care and it is slavery.
Society still has to cover much of the cost of support for that person and his or her family. Minimum wage workers require subsidized health care, subsidized food and subsidized rent. People at that wage level are often forced to engage in criminal activities to supplement their income so that children can eat so society is also required to spend more on policing and social services. And, where there is crime there are gangs and that adds to the social burden, too.
But, corporations win so we stick with the canard. Somehow we are convinced that there are tons of unskilled workers being employed to do things that the business can live without. The theory is that a business will spend large amounts of capital money to automate jobs rather than give more money to poor people. It is a ridiculous idea. Most low wage jobs are not really subject to automation (have you ever seen a robot janitor?) and, of course, the research does not support this idea anyway.
It is another conservative effort to make sure that workers are poor and afraid. Paying them a decent wage will only make them prosperous and unafraid. Better conditions, better benefits, better hours, better lives. The horror!
Paying unskilled labor a decent wage would demonstrate that people have value beyond the value of their work. Americans don't want that. Americans hate poor people.
So don't clothe your moral distaste for those less fortunate in economic theory. Stick with the real reason: People who don't have important economic skills are worthless and deserve shitty food and bad lives.