If the MW were to be raised to $15/hr tomorrow, or even by the end of the year, it would cause some disruptions in the low value business market. This is why a gradual increase has continued to prevent potential shock, more so than it has kept minimum wages up with inflation.
It is not very unreasonable that the rich should contribute to the public expense, not only in proportion to their revenue, but something more than in that proportion.
"Wealth of Nations," Book V, Chapter II, Part II, Article I, pg.911
I think many agree $15 is too high. That would cause massive job loss but a raise to $9 or perhaps even $10 over a 4 or 5 year period is reasonable. I think many asking for the $15 are hoping to "compromise" for a $10 wage when that is what they've wanted all along.