Most Mexican immigrants do jobs most Americans wouldn't do even if [their] life depended on it, like back breaking day labor for minimum wage sixty hours a week.
Immigrants steal life giving resources and land.
Any invasion by an alien society entering an established land. Europeans killed the new world indigenous peoples. Germans into Russia, Dutch into Africa, Brits into Australia, Brits vs Boars, et cetera.
Once one group of peoples establish a land as "Theirs" you have problems.
Be it Religious, or Purity of Race, every people of a land hates new comers.
And once the New Comers establish themselves it starts again.
Examine 'Texas' as a starting study of how society grows from immigration.
(The Wheel of Time rolls and will roll over you too.)
Your post brings a very interesting twist to the usual immigration debate.
I do completely agree that competition for land and resources is a significant issue in politics - in fact I'd go as far as saying one of the primary driving forces of politics in most of human history. I'd like to say it will always remain so as long as human nature remains as it is, but the same kind of competition is also prevalent in animals and even plants, so it is a natural part of life it seems.
However, I would disagree with your claim that immigration represents such competition. The immigrants in the US are hardly forcefully taking the land and resources of the people there. Also, the most valuable resources within the US - the multi-billion dollar corporations, the US armed forces, etc. are in no danger of suddenly falling into the hands of any impoverished Mexican immigrants.
Even if we are to assume that the presence of immigrants in the US (or other economically more developed nations) does indeed deny nationals of land and resources via competition, what is so wrong with it? While it might negatively impact some people by taking their jobs, it wll greatly advantage the American companies hiring less-than-minimum-wage impoverished Mexicans as opposed to higher-wage American workers (in reality the immigrants will fill job positions which wll otherwise be left empty).
Also, as you have correctly hinted, asides from national (or racial, religious, etc.) politics, there really isn't any ethical justification for favouring people born on one side of the boarder over those born on the other when it comes to job competition.