As far as I know, no one is saying that minimum wage laws are necessary in order to get people to work. Instead, the reason people (other than economists) usually support minimum wage laws is because they believe that businesses will pay workers the kinds of low wages the workers got back during the Industrial Revolution (and into the early 1900s in the US). Minimum wage supporters believe that it is wrong for people to be paid very low wages for their work.
The more interesting question here is "if there were no minimum wage, would employers pay the kind of low wages they did back in the old days?" In answer to that, an economist would say that people are more productive these days and so employers can pay them more. In addition, they'd say that good workers will be able to command decent wages because companies will need to pay them well to keep them from leaving to take other jobs.