Considering he did it for contracts the amount of work being done doesn't change so the idea that it kills jobs is unsubstantiated.
Mainly a symbolic move. Most employees of contractors get more than minimum wage. So it will have little effect on these employees.
Likewise, there is guaranteed demand in a federal contract. So there will be no job loss.
In the private sector, we should be honest about the subject. Yes there will be some job loss, but at the same time, some of the working poor will see their pay increase.
When you increase the cost of something, you lessen demand. That's the main idea behind sin taxes. But, increasing the cost of labor doesn't affect the demand for labor and/or increase costs?