“Common Sense” – aka knowledge held by the common man fails in this argument. The LA City Council studied 3 peer reviewed studies before increasing minimum wage. I don’t know what they read – but here is some of what I found.
Neoclassical economic theories present a clear prediction: as the price of labor increases, employers will demand less labor. However, many recent studies testing this prediction have found very small to no effects of the minimum wage on the level of employment – from Texas A&M (where my dad went) http://econweb.tamu.edu/jmeer/Meer_West_Minimum_Wage.pdf
Based on the economic multiplier effect that results from putting additional income in the hands of lower-income workers, raising the minimum wage will likely have a modest but positive impact on job creation, leading to an additional 85,000 net new jobs when fully phased in. http://www.epi.org/blog/raising-federal-minimum-wage-will-not-lead-to-job-loss/
If I see one more armchair Economist tell me differently I am going to ask them what they think happens when you blow in between 2 balloons. They will say they separate and I will say they touch. Sometimes what seems like the logical answer must be put to the test to find the truth.