But isn't he allowed to give an Executive Order? Wasn't that one of the measures that was put in for just such a situation as this? Unless you are saying that you don't believe the concept should exist at all and should be changed, I mean, it does exist and for this very reason. I guess I just don't understand the more moral frustration like he is doing something wrong. He's doing something that he is allowed to do. I understand better if people don't like that he's allowed to do it in the first place, but that's not on him. He didn't invent the ability to make an Executive Order himself. Or did he? I actually don't know and maybe I'm just making assumptions here about your politics.
In a nutshell, Presidential Executive Orders were intended to be policy directives to branches of the U.S. government (i.e., how agencies would run things, what their priorities would be, etc.). They weren't intended to be de facto issuing of new laws. So for example, the previous immigration amnesty bill (the Immigration Reform and Control Act of 1986) was passed by Congress. For the President to do what's being rumored, and issue an amnesty order himself, is effectively giving him the power to pass new laws.
Of course, the power to issue orders to the military and federal agencies concerning how they will do their jobs does involve a certain amount of legal interpretation or even, loosely, creation of "law." So there is a lot of gray area here, and why the powers of EOs have been increasing since the Bush administration, IIRC.
Is what he's doing strictly legal? Maybe. It might eventually take the Supreme Court to decide that. But it's dangerous to blithely say it's okay for the President to perform the functions that are supposed to be Congress's, just because Congress is being uncooperative.