Is there a reason why a $15/hour minimum wage would not function something like a helicopter money drop (http://www.economicshelp.org/blog/5937/economics/helicopter-...) and be helpful in times of low inflation (e.g., now)?
Raising the minimum wage does the opposite. Hiring workers becomes more expensive and 70% of that increase in prices is empirically passed on to consumers in the form of higher prices. So now the money to price ratio goes down and aggregate demand decreases. Your plan was tried in the Great Depression and it backfired spectacularly.
This depends entirely on the price elasticity of demand.