One of the easiest and most effective ways to discredit those who support illegal/massive immigration is to point out that many of them are engaging in false compassion: they pretend that their proposals are the humane choice, when the opposite is true. If an advocate supports false compassion, go to one of their public events, ask them a question on video based on what follows, and then upload their response to video sharing sites.
For a clear example, there are only two ways to sharply reduce the numbers of border deaths (those who try to cross the southwestern desert into the U.S. and who die along the way): either by declaring completely open borders and passing out citizenships to all who ask, or by stringently enforcing our immigration laws on the border and in the interior.
Anything between those two poles will lead to some people trying to cross the desert, and some of those won't make it.
Since we're never going to have completely open borders no matter how much an extremely small group of people want it, the only other solution if one wants to prevent border deaths is to stringently enforce our laws.
Yet, those supporters of massive/illegal immigration fight tooth and claw against most forms of enforcement. They are in effect daring people to cross the desert into the U.S. and sending them the message that if they can make it across the border they'll find a support network. Those supporters are like a neighborhood sociopath who thinks he's doing a good turn for the neighborhood children by cutting a hole in the fence surrounding an attractive nuisance such as an abandoned swimming pool.