I love this question. Mostly because what seems like should be a simple thing to answer, isn't. There are certainly strong opinions and much data that support both sides, however.
Neoclassical microeconomics (mostly like what one sees in mid-level undergraduate courses) suggests a minimum wage gives a kink point in individual's budget constraints--implying people may prefer to stay at minimum wage jobs rather than trade time for higher wage jobs, based on preferences. Additionally, if minimum wages rise too high producers will choose to replace labor (people) with capital (machines)--Stigler's argument.
Neoclassical macroeconomics suggests that minimum wage increases may result in inflation (more dollars chasing same number of items), black markets (e.g. hiring illegal immigrants or paying wages under the table), and so on. It is seen as a market distortion.
Labor economics and other sub-fields grant more nuance to these simplistic views. In the simple assessments above, minimum wage policies are at best set up as policies generating economic inefficiencies, at worst painted as immoral policies to support lazy people.
However, we do not live in a neoclassical world. Debates about the economic consequences of minimum wages are still hot topics, decades after they were first engaged, with supporting and detracting evidence. Wikipedia's coverage is a good entry point.[0]
For myself, I tend to come near "Bleeding Heart"/Arizona school libertarian when it comes to social policy--fiscally "conservative" (in that I want to make sure taxes are spent efficiently for the "best" outcomes, which we collectively decide is best), socially liberal, and a foreign dove. The toolkit of analysis emanating from economics does not immediately identify or lend itself to some superior moral framework -- that's on each person to choose themselves. Economics simply helps you identify where waste can occur, whether in the form of bias, inefficient capital deployment, risk, etc. For me, I sleep better at night knowing that my neighbor can afford healthcare and that the janitor I see working tirelessly can put money away for a rainy day.
Some of the more accessible discussions have happened on Barry Ritholtz's blog[1], where one of his contributors defend's Seattle's raising of the minimum wage and resulting impact.
Yes, this is a great example of how naive neoclassical micro appears to get things wrong. So, my argument is that given the malleability of supposedly purely descriptive and value free economics, the intrusion of politics is inevitable.
