Scaling the minimum wage to adjust for inflation is actually a good thing. The major drawback of raising the minimum wage is that it increases the price of human labor, resulting in lay-offs and unemployment.
The counter-argument to that latter point is that companies will create more jobs in the long-term by anticipating an increase in consumer demand among minimum wage workers. At this point, I'm pretty much convinced that there is no study that presents all of the data without a clear bias one way or the other.
My economics professor wrote a paper about this and he believes that raising the minimum wage to $15 dollars and hour is not only do-able, but will have little impact on unemployment, if any at all.
He argues that raising the minimum wage to $15 would:
1) Increase worker production and reduce employee turnover
2) Prices of products or food (such as a Big Mac) would increase, in total, by less than $1 and since the price increase is so small, it would have little impact on demand
3) Fast food (since his article focuses on fast food) is a growing industry and increased wages would only slightly decrease the annual growth rate
He claims that raising the minimum wage to $15 (specifically in fast food) wouldn't cause businesses to shed workers or experience large decreases in revenue