The American Conservative has a lengthy article arguing for a raise in the minimum wage from a conservative perspective. A couple of highlights:
Although the direct financial benefits to working-class Americans and our economy as a whole are the primary justifications for the proposal, there are a number of subsidiary benefits as well, ranging across both economic and non-economic areas.
First, the net dollar transfers through the labor market in this proposal would generally be from higher to lower income strata, and lower-income individuals tend to pay a much larger fraction of their income in payroll and sales taxes. Thus, a large boost in working-class wages would obviously have a very positive impact on the financial health of Social Security, Medicare and other government programs funded directly from the paycheck. Meanwhile, increased sales tax collections would improve the dismal fiscal picture for state and local governments, and the public school systems they finance.
Furthermore, as large portions of the working-poor became much less poor, the payout of the existing Federal Earned Income Tax Credit (EITC) would be sharply reduced. Although popular among politicians, the EITC is a classic example of economic special interests privatizing profits while socializing costs: employers receive the full benefits of their low-wage workforce while a substantial fraction of the wage expense is pushed onto the taxpayers. Private companies should fund their own payrolls rather than rely upon substantial government subsidies, which produce major distortions in market signals.
Public policy experts sometimes glorify complexity, proposing intricate, interlocking systems aimed at a desired result. But such structures are only as strong as their weakest link, and a proposal too complex to fully understand is also too complex to fix. Our government has sought to ensure a decent living for American workers through an enormous array of income subsidies, public benefits, training programs, and educational loans; at this point, many of these components have accumulated powerful and parasitic side-beneficiaries while leaving the working class behind.
Since this vast and leaky conglomeration has failed at its intended goal, perhaps we should just try raising wages instead.
Reducing the quoted material to its essence, the argument has 3 parts. First, raising the minimum wage will help the economy and the federal budget by increasing demand and tax revenues, by reducing the amount government pays out in various subsidies, and by strengthening social programs like social security. Second, it will be simpler and less costly than the ungainly patchwork of programs necessitated by poverty-level wages.
Third (and in my opinion most compelling), it will require employers to pay their own workers (and not so incidentally, compete with others in the market on equal footing) rather than depending on taxpayers to subsidize those wages as we do now.
Back when the GOP was a genuinely conservative party, it would have understood–and embraced–these arguments.