Noah Millman points to some basics about the role of the minimum wage as part of a conservative approach to a more just society.
In principle, any kind of “one-nation” conservatism has to care about inequality as such, and particularly about the weakness of labor’s bargaining power in most of contemporary America. Right-wing individualism is often conflated with a conservative approach to governance in contemporary American politics, but that conflation is a profound error. As a practical matter, I’m convinced that wage stagnation is the deep reason for the financial crisis. The Bush-era answer to stagnating wages was cheaper credit. That papered over the problem for a while, but it teed America up for a terrible crash. … Avoiding a repeat requires fixing the structural drivers of widening inequality, and particularly means raising wages at the low end of the scale. In that context, a legislated rise in the minimum wage should absolutely be on the table for discussion.
Wage stagnation is a serious economic and social problem with far-reaching consequences. You don’t get to say “I don’t care about that problem” because your ideology doesn’t have a ready-made answer. That applies to free-market-oriented conservatives and client-service-oriented neo-liberals alike, because solving the problem is going to require solutions from the “left” and “right” side of the policy box, and these solutions may be more complementary than contradictory.
In short, there’s something for everyone to contribute.