Recently, the Federal Reserve Bank of Cleveland published a Q&A where they suggested that raising the minimum wage won't reduce the poverty in America. One argument for raising the minimum wage is that income growth will continue to outpace minimum wage increases. Thus people being paid at the minimum wage level have actually seen their buying power decrease over time. In contrast, people against an minimum wage argue that it will lead to job cuts. Cleveland's Fed suggests a more targeted approach to reducing poverty.
See "CLEVELAND FED: Raising The Minimum Wage is Bad News For America's Poorest", Bob Bryan, December 3, 2015