Jaun has a couple advantages, in that lower skilled workers cannot compete with Juan on pricing. Americans are stuck with a price floor or minimum wage.
It is illegal for me to work for below the minimum wage, therefore, Juan can undercut me to gain employment as it is easier for one with no prior employment history to gain "under the table employment" than a person who previously enjoyed the luxury of the AMT. Had Juan have to compete of the same price floor, then our abilities would be the basis for competition.
Americans are harmed because they cannot compete. In the retail world (which hire many of these undocumented workers) it is often considered a "race to the bottom". If one company is allowed to employ these undocumented workers and another is not, wouldn't the first company enjoy a comparative advantage? A rational company would either lower prices such that the second company could not compete or enjoy healthier margins which allow for investments that the second company could not.
I am for immigration of any kind. However if Juan wishes to gain employment in this country his must be forced to compete with me on an equal playing field. He should not be able to enjoy the advantages of his undocumented status by undercutting me in the competition for employment.
I however bask in the comfort of being skilled, technical labor. No mexican crossing the river can do what I do. Primarily because my occupation requires you to be a born citizen in the United States (naturalized need not apply), and secondly my skills would warrant a greater wage in Mexico (comparatively) than they would in the United States. It would be actually be to my advantage to emigrate to Mexico and compete the them as my skills are in lower supply.