Funny. I just, not even thirty minutes ago, go through discussing something very similar on Facebook so I'll just post here what I posted there...
Frankly, I don’t have the answer to the question about illegals; however, the last I checked we had a constitution that split the power of the federal government into three branches. I honestly haven’t read the constitution in several months, but when I did last read it I don’t remember a single section that granted the head of the executive branch the power to do whatsoever he pleases. The guys who wrote and signed the thing actually had fought a war against such a situation not very many years before the document was created so I’d have to assume that they wouldn’t really cotton to the idea.