Beyond the basic lunacy of attempting to help the poor by mandating that they sell their labor for more than most businesses are willing to pay, I am reminded of another problem with proposals for a higher national minimum wage.
This problem is related to one that is seldom discussed in the context of most economic statistics, and that is the differences in the cost of living in different parts of the country. The Tax Foundation looks at the cost of living by state, showing the value of $100 ($100 is worth more in states with lower prices and cost of living, since one's money will go further). Magenta states are lower cost of living, yellow states are higher.
I have written before that not taking this into account messes up our view of things like poverty and income by state. Well-being of folks in high cost states like California and New York are often exaggerated, as is poverty in states like those in the deep south.
But another issue is that this large variation in cost of living changes the effective value of a minimum wage. Based on these numbers, a $15 minimum wage in Washington DC becomes, effectively, a $20.43 minimum wage in Mississippi. Employment effects are likely to be much worse in these lower costs states. Since the higher cost states all vote Democrat in Presidential elections, and the lower cost states all vote Republican, one wonders if this is a bug or a feature of Democrat-proposed $15 minimum wage plans.