One other thing:
IF raising the minimum wage resulted in inflation, so long as the minimum wage was pegged to that inflationary number, since the wage floor would rise, everyone's wage would rise. So, the person who can buy what a million dollars buys today will still have that buying power, since their wages would rise as well. It may be $1.5mil vs $1 mil today, but they wouldn't be disadvantaged.
However, I don't think prices would raise all that much. Rather, other things would be done to try and keep prices where they are (since runaway inflation will affect businesses in other ways). More reliance on automation is one already mentioned. Another is companies creating other revenue streams to compensate. So, McDonald's may start to charge you for straws, bags, and the like. You don't use a bag, you don't pay. But most will.
An example of this is Aldi's. They not only have good, quality food at cheap prices (again, research the quality of their food; I was amazed), they also pay their workers some of the highest wages in the supermarket industry, with good bennies. How can they do this? You buy bags from them. Their stores have a very basic setup. No credit card transactions (and thus no credit card fees, although they do take debit).
Our very own UPS is another example. We moan and complain about how they just pour work on us, and all the reports they watch us on now. However, I realize this is one way they try to compensate for our industry - leading wages. Hence, not only do I not complain about these, I am one of the "fools" who tries to meet their numbers. I don't go crazy, but I enjoy my wages and will work to keep them.