Gary Becker and Richard Posner have good posts on the minimum wage at their blog.
In watching this debate unfold, I am moving toward the view that the issue is more symbolic than substantive. Posner asks, "why are the Democrats pushing to increase the minimum wage rather than to make EITC more generous?" Here is my answer: Many voters don't know what the EITC is, whereas the minimum wage is easy to understand. As Becker points out, "Most knowledgeable supporters of a higher minimum wage do not believe it is an effective way to reduce the poverty rate." True, but few voters are so knowledgeable. As a result, the minimum wage is an easily explained issue that says, "We Democrats care about poor people, unlike those Republicans."
Here is a question that I would ask any politician: If you could set your ideal policy to help the poor, wouldn't you prefer to expand the EITC and abolish the minimum wage? Any politician that fails to answer "yes" is either misinformed or engaging in demagoguery.