The wording of the question leads me to respond with "the gap itself isn't an issue". I don't consider an income gap to be inherently bad, but I think the various nuances that accompany our existing income gap are bad.
Our political policies and tax rates are actively encouraging the income gap to grow, and harming quality of life for a large portion of Americans. If we agree that we want to tax income, then we cannot create and maintain policies that allow a higher income individual to pay a lower portion of their income in tax. That's just the basics.
When healthcare, SNAP and social security find themselves on the chopping block, lower income brackets find themselves riddled with risks and decrease consumption of staple goods (thus harming the production and profitability of staple goods). The political engine that is funneling money from the lower income brackets towards the higher ones is holding back the economy.