In time that is correct, however, initially it would impact unemployment. What raising the minimum wage doesn’t do is create what people call a living wage, at least not in the long run. That’s because everything will rise along with that minimum wage, creating inflation, and in very short order those making minimum wage are in the same situation they were previously. History has proven that axiom to be true. It’s like raising the IQ standards, those that are 50 will be 150, but they will never catch up or be any better off than those with 400 IQs.
If you keep this attitude then the Republican Party will always struggle with getting the working class. The Republican Party will always be a minority party with few exceptions. This is a political and not just an economic issue.