When discussing undocumented workers many people on both sides of the argument make the claim that these workers end up in jobs "Americans don't want." However I think this argument places the decision making wrongly in the hands of the average American, who in this fantasy considers themselves too good for farm work or that it is too difficult work. It seems more likely that the reason these jobs are not taken by Americans is because the companies that hire these workers would be completely uncompetitive if they hired Americans (due to their ability to demand better pay and protection). Only through hiring marginalized workers with no formal rights are they able to remain competitive with goods produced much more cheaply elsewhere.
There are many jobs that are much more disgusting and backbreaking than field work but are done by Americans and some are even unionized. This is possible because these industries can remain competitive despite paying reasonable wages due to different competition structures than is present for agricultural work (e.g., copper mines). Many of these companies would have already moved production to another country if possible; but they are unable to, due to the type of product they produce.
While this argument leads some to push for new policies of protectionism, for me it indicates the need to structure trade in a fair way. Protectionism has done little to provide good long-term jobs for Americans. We must come to the point where the lowest cost is not separated from the factors from which the product are produced. Products from countries with substandard quality controls, unethical work practices, and terrible human rights records must be identified as such. By accepting these products despite these problems, we are just serving to reinforce the negative tendencies under which the goods were produced.