Well as I said things have and always will be about money. American citizens willing to work for less than minimal wages are free to do so as well. They can certainly ship their family in some other country with low standard of living (I'm sure with enough cash flowing from US they won't even need to learn the local language) and then they can share an apartment 50-way instead of 30-way and undercut the illegals.
A couple of states happen not to have minimum wage laws so that would seem doable at least in principle.
Of course US government can institute protectionalist policies as John suggested and send inspections to other countries to monitor the wages, working conditions etc... But what guarantees that the other country would accept US inspections? Another way is to just stop international trade whatsoever - only US produced goods will be allowed to be sold on the US market. That is also not a good solution.
I've seen some people boycotting companies who are deemed immoral. That really is the only way to solve this, but it requires enough people to be willing to voluntarily pay the cost of not purchasing certain products. The mechanism is there, but it's not used, so the result is what we have and that will continue. Just because people are primarily selfish and would like everybody else to pay the cost, while they share in the benefits. I don't think it will change anytime soon.
To my mind globalization is unavoidable and outsourcing is similar to a US company moving to another state where the economic conditions are more favorable, but on a more global scale. I threw in the outsourcing thing just because when the economy was going well and almost every american citizen could get an office job nobody cared that their lettuce was picked from an illegal immigrant. I've given that example before - a friend of mine comes from a farming family in CA and according to his dad those of mexican origin are way way more motivated, hardworking and honest those who speak fluent english. And as far as summer jobs go, I have plenty of college-aged relatives who are working each summer in various low skilled jobs in US and Europe. 16-hour days 7/days a week at a mimimum wage, living in barracks. Of course the few thousand dolalrs they earn from doing that is quite a different thing in where they come from, than where a US citizen will normally spend their money. But that's how it is - the standard of living in various parts of the world is different and both workers and employers can exploit this inequality. Perhaps in the long term the gaps will close a bit, who knows. But I don't think anybody has a good solution where everybody is happy. In such situation I personally would put my bets on being as competitive as I can on a global scale and then I can continue doing what I like to do and not have to compete for the lettuce picking jobs out there (it's not that I haven't done such jobs).
I guess different countries like to do things differently, but going after employers and employees seems rather backwards to me. If you care about your national security you protect your border with military. US has only 2 land borders, most countries have 4. Of course most countries are also more densely populated, but if a state cannot protect its borders it really deserves its neighbors to cross them as they see fit. The US-Mexico border is about 2000 mile long. It seems reasonable to me that 50 soldiers is more than enough to protect each mile, which would require 100 000 soldiers. US has a lot more than that in various foreign countries, which tells me that it's not the lack of personel, but the lack of will that is to be blamed.
So, yes, the illegal aliens are criminals, the people who employ them are criminals as well, but what are the political leaders who have failed to protect the US border? What about the voters who elect them? If memory serves there was at least one presidential candidate who wanted to secure the US border - he didn't seem to enjoy all that much support. The same is true even on a smaller scale of local governments.