These people disagree
Source USA.gov.What is a presidential executive order?
An executive order is a directive by the President of the United States that has the power of a federal law. Presidents might issue executive orders to create committees or organizations like the Peace Corps. In general, though, Presidents use executive orders to direct and manage how the federal government operates.
Congress specifically delegated to the AG the ability to make exceptions for illegals as he sees fit. congress delegating it's nominal responsibilities to executive agencies is commonplace. It happens all the time.