Every single restaurant in Pasadena has had to contend with the same issue, and every single restaurant isn’t going out of business. So quite frankly, I think a glib, off-the-cuff response is perfect for such a ridiculous assertion.
Furthermore, the lone study you cited contains this very important line:
First off, there are only 24 hours in a day. If someone is working full-time for slave wages, they cannot support themselves let alone a family. There simply isn’t enough time in life to get 2nd, 3rd or 4th jobs at paltry wages to scrape by. So the minimum wage increases…and their hours get cut? Okay, well they at least have some free hours to work a second or third job or maybe even develop their skillset in the short-term with the new free time and free or low-cost job skills development courses. The position gets eliminated completely? Good thing unemployment is really low now, so they should be able to find something that pays at least the minimum wage somewhere else.
Also, people at the lowest end of the economy tend not to save much at all, so every additional penny in their pockets generally goes back into the economy in the form of consumer spending. That’s why trickle-down economics doesn’t really work all that well: giving more capital to the top in the form of tax breaks doesn’t get reinvested directly into the consumer economy as much because the well-off tend to invest extra capital into stocks or other savings investment vehicles, which while that does have a positive impact on the economy, it is NOT as beneficial as direct retail and/or service sector spending.