Raising the minimum wage probably does cause less work time and inflation in the short term. But as long as the employer is running a profit and the demand for labor is reasonably elastic, the increased wages transmitted to workers will outweigh that loss for other workers, for a net gain overall on the labor side. This has the added benefit of, through those laws of economics you cited, enticing more lazy freeloaders back to work, since they can get more money. Lastly, with the increased spending power possessed by consumers, demand increases, allowing businesses to gain back some of their losses from the higher minimum wage. The end result is an initial increase in the demand for jobs and a decrease in the supply of jobs, which is later offset by an increase in revenue that leads to an increase in demand for labor by businesses.
In short, the cost of a higher minimum wage is shared by businesses' profit margins, employees with hours cut, and the economy at large through inflation, while the benefits are shared by low-wage workers, and businesses through increased revenue.
