In my opinion, almost all of the actual past raises to minimum wage have been on the small side, and have not significantly affected unemployment. You're right about that.
But if my opinion is true, then there's a huge leap with no scientific basis to saying "therefore this specific large increase in minimum wage will not raise unemployment."
Unfortunately, there aren't any scientific studies of increasing the US minimum wage by 100% because it has not been done multiple times in the past. So no one really knows what would happen if we did it now.
I figure you made your comment to demonstrate that the reasoning doesn't work on the extremes, but that only really works as a rebuttle if someone were seriously suggesting something extreme.
These would have ripple effects up the chain. Malls and retail real estate are empty as it is, for one; any fewer and we legitimately might see problems.
Assuming that's accurate, then shouldn't we mandate that these corporations pay their workers a livable wage? If they don't pay the workers a livable wage, guess who does? The taxpayers, in the form of food stamps, welfare, and increased prison population. I really don't see why the American public should be forced to subsidize Walmart (or any large megacorporation) just because they won't pay their employees enough.
[0] https://en.wikipedia.org/wiki/Minimum_wage#cite_note-104 [1] https://en.wikipedia.org/wiki/Minimum_wage#cite_note-105
EDIT: Before anyone says it, I know forcing Walmart to pay more to their workers would increase the prices of their goods; that's still almost certainly cheaper than increasing welfare.