Without getting into a discussion on what it should be, what's fair and all that. I just want to discuss what happens when it goes up. Based on my experience hourly employees value themselves on how much over the minimum wage they make. When it goes up those people want to get a raise so they maintain that difference. They will be unhappy and feel underpaid if they don't get that raise.
Raising the minimum wage has more of an impact than most people grasp. Some people don't understand this, they think statically. They don't understand the effect changing something as fundamental as this will have. They just assume this extra cost will come from employer profits. What actually happens is quite different. Businesses have to maintain a certain profit to stay in business. When a cost goes up they have to offset that by cutting costs or raising prices. Raising prices is never a good idea because when something is more expensive people buy less of it. That would kill the business. So cutting costs is what is usually done. That means cutting the labor costs because other costs usually can't be cut, rent, utilities, etc. They will cut labor costs by a combination of shorter hours, eliminating some jobs and asking people to work harder to get the job done. The effect of all this is that workers on the low end of the wage scale will be the first hurt which is exactly the people the proponents of raising the minimum wage want to help.
