Um, according to standard economic theory in the long-run equilibrium the unemployment rate is the rate of frictional unemployment and that is more-or-less of a constant. What we have is cyclical unemployment, which is temporary. http://en.wikipedia.org/wiki/Unemployment_types
Look, someone who doesn't have a job will lower his/her price until he/she gets a job. If you are really on the verge of starvation you will become willing to work for $1, and someone will probably become willing to hire you for that little. Just like any other market, price will fluctuate and equilibrate supply and demand, clearing the market. It's just that in the short run there is price inflexibility, so the market temporarily goes out of whack. In the long-run wage is only determined by worker productivity (which is function of amount of capital and technology level), and anyone who wants a job can have one, though it may not be as high paying as she wants.
The price inflexibility is deeply ingrained in housing prices, and the regulation by the state. No matter how desperate you are, you cannot legally work for as little as someone in many foreign lands.
We are not even close to there yet. If that does become a problem, if min-wage causes 30%+ of the workforce to be unemployed, the government will lower it. They are stupid, but not that stupid. Besides, housing prices are also shaped by supply and demand. If unemployment becomes very high, housing prices will drop. Essentially what you are talking about is short-run price inflexibility.
"They are stupid [ the government] , but not that stupid."
Don't count on it. There is something about government that attracts and concentrates stupidity. They discount reality, blank out unintended consequences, operate with stolen wealth, and shift blame AND cost for its failure onto its victims. In that environment its almost impossible not to be terminally stupid.
The problem is that 'standard economic theory' is not in complete agreement here. As the article you linked says, classical economists (whose argument about the market clearing is the one you put forward) do not believe in cyclical unemployment. Those who do believe in it don't believe that the employment market clears of its own accord.
A separate issue is that people can't lower their wage demands to any level. To get a job you must have a home, a means of commuting and the basic necessities of life. There are also costs associated with employing someone, so even if someone worked for free, the employer could not necessarily justify the cost of employing them.
These are theoretical issues though. The existence of unemployment benefit means that the only people who will reach these depths are the homeless.
Look, someone who doesn't have a job will lower his/her price until he/she gets a job. If you are really on the verge of starvation you will become willing to work for $1, and someone will probably become willing to hire you for that little. Just like any other market, price will fluctuate and equilibrate supply and demand, clearing the market. It's just that in the short run there is price inflexibility, so the market temporarily goes out of whack. In the long-run wage is only determined by worker productivity (which is function of amount of capital and technology level), and anyone who wants a job can have one, though it may not be as high paying as she wants.