There's no solid evidence that increasing the minimum wage will create fewer jobs. From Paul Krugman's review of Robert Reich's new book
> Other evidence points indirectly to a strong role of market power. At this point, for example, there is an extensive empirical literature on the effects of changes in the minimum wage. Conventional supply-and-demand analysis says that raising the minimum wage should reduce employment, but as Reich notes, we now have a number of what amount to controlled experiments, in which employment in counties whose states have hiked the minimum wage can be compared with employment in neighboring counties across the state line. And there is no hint in the data of the supposed negative employment effect.
> Why not? One leading hypothesis is that firms employing low-wage workers—such as fast-food chains—have significant monopsony power in the labor market; that is, they are the principal purchasers of low-wage labor in a particular job market. And a monopsonist facing a price floor doesn’t necessarily buy less, just as a monopolist facing a price ceiling doesn’t necessarily sell less and may sell more.
http://www.nybooks.com/articles/2015/12/17/robert-reich-chal...
There's also something similar to your subsidy idea today called the Earned Income Tax Credit [https://en.wikipedia.org/wiki/Earned_income_tax_credit]. Guaranteeing a minimum income does seem like a promising idea, but it will probably have to be tried elsewhere before the U.S. will adopt it (if ever).