No, it's an accurate, dry, legal characterisation of someone present in the country illegally, much like referring to someone who has murdered someone else as 'a murderer,' or to someone who has shoplifted as 'a shoplifter.'
I'm actually philosophically inclined towards completely open borders (although I have some deep concerns about what that does to community & culture), but an alien who is present illegally is truly an illegal alien. Words mean things, and that's what those words mean.
I want to put this on the biggest billboard I can find, or put it in Nazca lines across the surface of the moon, so maybe we'll remember. Language lawyering is profoundly useless, and I've no patience with it.
There is a lot of implied sub-communication that comes with word choice in human languages. Only an idiot or a robot would take everything by its literal meaning.
If everyone is free to redefine words to mean whatever they damn well please, then it is impossible to have clear, effective discussions, because you get wound up wrangling about definitions - as we do habitually here, talking past each other.
The truth is that the people behind most of this anti-immigrant rhetoric can't see the humanity of someone who is not of their same skin color. When they call a human being "an illegal" -- it's dehumanizing, and it plainly reveals they don't see their common shared humanity. I've noticed it in the language they use, and they way they talk about other people -- and not just immigrants, but black Americans as well. They simply do not see other races as people like themselves.
I absolutely do not think that Luis Gutierrez is someone that is just looking out for "his own people", as you seem to be implying.