I think, at the end of the day, the minimum wage is a mediocre mechanism of eliminating poverty. If you raise it to a level like $10 - $15, you're going to have a significant amount of job losses and job prevention because of rising costs, so you're effectively making the poorest (i.e the people who need it most) unemployed.
Having said that, eliminating the minimum wage is only an answer if its replaced by a better system. Evidence seems to suggest that the Earned Income Tax Credit (and similar systems) is a better mechanism that can provide additional income to the poor at the same level of the minimum wage, but at significantly lower cost. The concept of the negative income tax I think is a better way.
Business owners need employees. Also, they have to follow lord-only-knows how many regulations and laws as is, so why not another?