One can reflect--as one must as a responsible citizen in a free society--strolling in a pasture, or even in a not crowded urban park; but as the population soars, that reflection is more & more challenged. One does not reflect very deeply in a bumper to bumper gridlock.
The duty of the United States Government must always be to its rooted citizenry; not to any foreign interest that might conflict with that first duty. Scratch an advocate of heavy immigration, and you will invariably find an internationalist, quite willing to deny the interests of his fellow citizens, while pursuing some humanist fantasy of a new world order.
I agree with you completely, however, that the biggest threat posed by Third World immigration isn't economic but cultural. We're importing a culture of poverty, ignorance, and crime by the millions when we allow Mexico and Central America to dump their social dregs on our side of the border. American middle class neighborhoods are being replaced by barrio culture thanks to our insane immigration policy, and what's happening in Europe thanks to immigration from Africa and the Arab world is even worse.
This is an important issue. There's an inverse relationship between population density and liberty in America. Rural, ethno-culturally homogeneous, low density regions of the country tend to be economically libertarian and socially conservative (in a live and let live kind of way). Dense "multicultural" urban areas are characterized by high taxes, high regulation, and social liberalism. Some of this is just social rot, some of it (such as anti-pollution restrictions or building codes/zoning laws) occur out of necessity.
Either way, you can't have Montana or Idaho-style communities when your cities look like Tijuana or Lagos.