Turns out they are against it.
I guess the whole idea of having a border is politically incorrect now, as is the notion that you even have the right to lock your own front door to whoever happens to want to enter.
Have we learned nothing from the past? Wasn't the lack of a defensible border what caused the previous owners of America to lose control? Ok, just kidding there, but really, now, a border is a must have and controlling who crosses it is just part of your right to exist on a piece of land unmolested by others. Previous crimes of this nature notwithstanding.
All that aside, a stronger border is not the solution. Getting rid of the distortions in our labor markets will decrease the cost of US labor and removing the citizenship-by-birth carrot will decrease immigrant willingness to put up with low wages.
But, even if we do nothing about this issue, is the situation all that bad? Getting across the border is dangerous to be sure, but otherwise I think everybody benefits. Even those that are getting more competition benefit, as we all do from competition.