You wouldn't suppose that might be because the two are entirely unrelated to one another, would you? If you want to argue that doubling the Federal minimum wage would cause prices to increase, that's fine -- and, in your defense, such a sudden and drastic hike might exert some inflationary pressure on some sectors of the economy, such as fast food and retail. However, I never advocated a $15 minimum wage.
If I'm even interpreting your post correctly, you're trying to argue that a doubling of the minimum wage would cause consumers to pay more in the same way that sales taxes cause consumers to pay more, in the long term. That's... nice, I suppose, but you didn't present any evidence to prove it. As noted earlier, wages are only one aspect among many to consider when discussing prices.
I also thought this part of your post was a tad bizarre.
"Ever hear of a sales tax? Of course you have. It's a SALES tax, not a PURCHASE tax."
Governments mandate that businesses collect a tax equal to, say, 6% of a sale at the point of purchase -- in addition to the cost of the merchandise. I'm not even sure what you meant there. It's fairly obvious that consumers are "stuck" with paying that tax, as you mentioned in your post. Why state the obvious?