When someone tells you that raising the minimum wage, or that having a minimum wage at all, eliminates jobs; the truth is that what eliminates those jobs is not the imposition of fair wages, but the unwillingness of companies to accept even a meager decrease in the net profitability achieved through exploitative wages.
When CEOs and other executives are paid up to 500 times more than the lowest paid workers, raising the salaries of those lower level workers can easily be accommodated by even a slight decrease in the exorbitant salaries at the top. There is no valid justification for jobs to be lost, nor for the prices of goods and services to be hiked.
If you want to talk about an income gap, you should be looking at the pay gap within corporations between the highest paid and the lowest paid workers.