There may not be an easy fix, but there are a few basic steps that lead in the right direction. Have you had a casual look at the links I posted? The effect you automatically infer from higher wages is not quite as clear cut as you might think. The world is a bit more complex than Econ 101. My understanding, from the little I recently read on the matter, is that the argument against a reasonable minimum wage is about at par with supply side economics: steeped in ideology, not quite so in reality.I don't disagree that someone doing an honest days work should not be living below the poverty line. However, there are some things to address in thinking that arbitrarily raising the minimum wage will bring these people out of poverty.
First I don't think we can raise wages without having an impact on price of goods and services. So what happens? The poverty line moves in tandem with that wage hike. Same people are still in poverty and this assumes that there will be no negative impact on the number of jobs. Secondly, we need to discuss what creates the poverty line itself. Is it just low wages? I don't think so. It's hidden inflation that we pretend doesn't exist. It's ridiculously high wages at the upper end of corporate America. It's inefficiency at all levels of business which causes price increase to cover that inefficiency. It's plain old greed, and yes, it's also plain old mis-management of the household budget by the working class. Add it all up and you have a broken system. There is no easy fix.
You're right, there is no easy fix. But allowing employers to squeeze employees with below subsistence wages is allowing the powerful to prey on the vulnerable. And how do you expect the vulnerable to better their lot and better contribute to society? They're fighting tooth and nail just to stay above water. You want to give people a chance to improve themselves and reach higher levels of employment? First, you need to give them room to breathe.