There seems to be an underlying assumption that unemployment is always a bad thing. Not only that, but that it is but such a bad thing that it is better to pay people less than they need to meet their basic needs, in order to avoid it.
This assumption is not well founded.
Unemployment is not necessarily and in all circumstances a bad thing. Until the introduction of social safety nets in the early 20th century, unemployment didn't exist. Those safety nets replaced poverty, which was truly awful, with unemployment, which was far less awful. The erosion of those safety nets since the 1970s have created a situation where unemployment persists, but poverty has also returned - a lose-lose situation.
From the point of view of the unemployed person, unemployment is bad if, and only if, it means an inability to meet his basic needs. This is only the case if there is an inadequate social safety net. With an adequate safety net, ideally one that includes the provision of training, unemployment is better than poverty, because the lack of money is compensated by a wealth of time to learn new skills.
From the point of view of the economy, unemployment is bad if, and only if, the people who are unemployed are reducing overall productivity through their unemployment - ie, if there was something useful for them to do that is not getting done; but if there was something useful they could do, that is worth the cost of their basic needs, then they wouldn't be unemployed with a MW set at the level that meets those needs.
From the point of view of employers, unemployment is great - it allows them to keep wages down. A MW is necessary to prevent them from driving it down to the point where their workers cannot meet their basic needs; but above the MW level, wage inflation is kept in check by the existence of unemployed people.
So even if (and this is far from certain), EVEN IF a rise in Minimum Wage was to cause unemployment, this is still not necessarily a reason not to do it.
A civilised society would include the following mutually supporting elements:
1) A minimum wage of around US$15/hour, with 'junior rates' for teenagers, starting at about 50% of the full MW at age 15, increasing with age to the full MW by the age of 21
2) A minimum unemployment benefit of around $300p/w for adults with no other source of income
3) Universal access to healthcare paid for through income taxation, and/or value added tax on non essential goods and services, with minimal or zero direct fees charged to patients for non-elective treatments
4) Universal education to the Bachelors Degree or skilled tradesman level, with education mandatory for all under 16 years old, and all unemployment benefit claimants under 25, also paid for from income taxation, and/or value added tax on non essential goods and services
All of this is readily achievable and affordable - indeed, this is pretty much how things are currently being done in many places, notably North Western Europe; those on the US East Coast may have noted the absence of severe Tsunami damage due to the collapse of that part of the world resulting from these basic humane provisions.
If you stop thinking of the unemployed as lazy slackers, moochers, and n'er do wells, and start behaving humanely towards them, you might be surprised to find that they stop bouncing from poverty compelled crime to minimum wage job and back again like badly abused tennis balls, and start using their periods of unemployment to gain marketable skills that get them into permanent and genuinely productive work. The overall economy booms, unemployment falls, and the remaining unemployed don't need to spend their days mugging old ladies or breaking into people's homes and businesses, just to put food on the table.
Why is this not already being done in the wealthiest nation on Earth? I blame the unfathomable Protestants, and their inscrutable 'work ethic'.