I don't know the answers, though I know the issues are multifaceted and that there is a great deal of human suffering. I also know that sometimes the side-effects are unthought of (e.g. Mexico has less pressure for internal change because the United States provides some relief -- enough to make a difference, I'm not sure).
I've a post on the topic at http://mormonmatters.org/2010/09/23/am-i-my-brother%E2%80%99s-keeper-undocumented-workers-and-illegal-aliens/
Of all things, I'm curious in what solutions people are proposing these days.