It is curious that some economists, like Harry Holzer, are so totally focused on the possibility that there could be some quantitatively small loss of employment due to a higher minimum wage that they implicitly downplay a wider universal finding: a higher minimum wage will substantially lift the average annual earnings of low-wage workers (because even if there is a small negative employment effect—which the weight of the evidence shows there isn’t—that effect is swamped by the much higher wage). Consequently, we know that low-wage workers and their families will be better off financially, no ifs, ands, or buts.
Further, the weight of the evidence does in fact show that the employment effects of increasing the minimum wage are indistinguishable from zero. There is a vast literature on the effects of increases in the minimum wage on employment that spans many decades and has gone through countless methodological improvements, with each new round of literature incorporating lessons learned from the last. In the last several years, a new series of rigorous, peer-reviewed papers on the effects of the minimum wage has been published in top academic journals, and represents the best in methodological practices (see for example here and here). These studies find that increases in the minimum wage have raised wages, but have had essentially no effect on employment, even in times when the labor market is weak. In other words, incorporating decades of work that came before, the state of the literature is that increasing the minimum wage improves the earnings of low-wage workers without significant adverse employment effects.
The figure below is from a meta-study of 64 minimum wage studies conducted between 1972 and 2007, which found that the most precise estimates of the effects of increasing the minimum wage were heavily clustered at or near zero employment effects.
Given that the increase in the minimum wage to $10.10 by 2016 is typical in size of past minimum wage increases, and the evidence shows that past minimum wage increases have led to employment effects that are indistinguishable from zero, it can be safely concluded that the evidence implies that increasing the minimum wage to $10.10 will increase the wages of low wage workers and not cause job loss.
See this paper by John Schmitt for a comprehensive review of the literature showing why the minimum wage doesn’t cause job loss.