The nations in which we live (America, Australia, etc) have a far greater standard of living than most other nations. That being the case, people who are willing to work for bread crumbs migrate illegally and subsequently take your job. The only way to combat this is to be willing to work for bread crumbs yourself, which will drastically decrease your standard of living, thus taking a once great nation down to the substandard level as the rest.
First of all, the current market is not a free one and not actually representative of what wages in a free one would be due to govenment intervention that most often favors big business. With an unfettered market, wages would likely be generally much higher due to there being no artificial barriers to entry and therefore more competition.
Second, while illegal immigrants are "willing to work for bread crumbs" they also have their bargaining power greatly reduced due to the fact they have to work under the radar. Without immigration laws they would be no more different from anyone else looking for work.
Third, immigration is also encouraged by government due to the welfare state. I am not saying that all immigrants come to the US and Australia to leech of welfare but if someone knows they can get free shit from the government people who would not otherwise immigrate, they probably will.
Finally, as the video in that post points out, the standard of living in their countries are due to the fact that their governments are even more corrupt and tyrannical. You can't solve problems created that way by becoming more like it.
I'm tired so this post isn't as eloquent as I hoped it would be.