Lazs, how else than via politicians whose responsibility it is could changes such as outlawing illegals be made?
I don't know about sorting thru the webs of corruption, but if political actions were squares on a table top covered with them, where each demand on one side would get in only by pushing another one off the table (this being metaphor-space, a system (aka tabletop) free of corruption would hold all the squares necessary, no more (aka small govt)), continually pushing for what the people want (which should be the right things) should come naturally (common sense) and receive no opposition from the politicians concerned, lest they admit they've got other interests, which if made to happen for their electors to see, would have them removed from their responsibilities.
It might sound naive, but my intended point is that if people were correctly informed and lucid enough, the politicians could only follow their will.
The truth can't be denied, and this instance is no exception. People naturaly do what's good for them. All they need to deal with what isn't is to have enough lucidity to get to the bottom of what that is.
e.g. just like the constitution originated from 'the people', ejecting such a tumor ought to as well, if for no other reason, because it is their sovereign right.