How out of bounds is the $15 California minimum wage?

By 2022, when fully phased in (small firms with fewer than 25 workers would have until 2023 to comply), the California minimum wage would represent 69 percent of the median hourly wage in the state, assuming 2.2 percent annual growth from the current median of roughly $19 per hour.

That 69 percent ratio would be all but unprecedented, in U.S. terms and internationally. The current California minimum wage represents about half the state’s median hourly wage, just as the federal minimum wage averaged 48 percent of the national median between 1960 and 1979, according to a 2014 Brookings Institution paper by economist Arindrajit Dube. (It is currently 38 percent of the national median.)

Other industrial democracies with statutory minimum wages typically set theirs at half the national median wage, too.

That is from Charles Lane.  This is also worth noting:

Dube, generally a supporter of minimum wages, recommended that states use 50 percent of the median as their benchmark in the United States. (He told me by email that California’s experiment is worth running and monitoring.)

Yet Alan Krueger, among many others, is against it.  On what grounds is it worth running?