Yes and no.
The problem is a complex one but raising minimum wage is a lot like raising taxes. In periods of good economic health, its impacts are hidden and negligable. In periods of poor economic health, they are noticable and strongly impactful. Over a period of time, the prices of products and services equalize the impacts of them. Who gets hammered the hardest is the small business with a handful of employees because they both do not have the market force to alter pricing to adjust and have the least capitol to float on while adjusting.we do know that a combination of raising taxes and interest rates tipped the economy over and started the great depresion.
Now where it is not like a tax is in that many businesses including small businesses already pay above minimum wage to most of their employees. Where minimum wage is most prevailent seems to be areas with a lot of unemployed and fast food joints. Low unemployment sort of forces employers to pay more in order to stop employees from switching jobs to get raises or the benefits they want.
So raising the minimum wage will hurt strugling economies more so than thriving economies. As an invester, if anything lowers my rate of return, i look for something else to put my money in. So until prices for goods and services equalize with the increased costs, you may find areas people refuse to invest in seriously slowing any recovery efforts.
But iit is not just taxes or minimum wage that can cause this damage. Increased energy costs and regulation can have the same impacts.