First off immigrants commit crimes at a lower or equal rate as natural born citizens this has been shown over decades of research. A small sample of such studies available here. So if you wanted to reduce crime resources would be better spent inland. As for the small section of immigrant criminals they will be easier to identify when you don't have millions of honest hard working people lumped into the same category.

Second, what I meant by more liberal immigration quotes is that you bring people into the legal system. This lets people live within law. There is not an infinite amount of people that want to leave mexico for the US... for many years we did not have a militarized boarder yet people where happy to live their lives in mexico. The influx of immigrants is a result trade policies, and globalization ... not people simple deciding on a whim to move countries to spite you and what you worked for.
Adjust the trade policies so that the disparity of wealth is not so dramatic and you will fix the immigration "problem" much more effectively.