The fallacies of Anti-immigration rhetoric

It is difficult to find people are arguing for a tough line against immigration without using it to make a larger point about American Identity and values. Lionel Shriver does exactly the same thing in his article by arguing that the American mythology of "the melting pot" is in part responsible for the fact that millions of people ac cross the world are willing to do anything to live in the United States:

The entire world seems to believe they have a right to live in my country, but it doesn't work the other way around; other countries are as defensive of their borders as they are oblivious of mine, and I bristle at the double standard. [...] Forever talking up the "melting pot" and our proud tradition as a "nation of immigrants", US politicians can't sabre-rattle over stricter immigration policies without sounding like hypocrites. The rest of the world doesn't believe the US has the right to police its own borders; raised on all that "huddled masses yearning to be free" folderol, Americans don't either. In short, the US has been helplessly victimised by its own bullshit

The problem with this kind of rhetoric is that it is based on false assumptions and on some prejudices.

Lionel Shriver is in fact arguing that the US is a victim of immigration because it has used it to shape its image. The problem with this argument is that the US has benefited more immigration than it has been hurt by it. It is impossible to study about American history without learning of immigrants who came to the US with nothing and who were able to live better lives. A good example of this is Madeleine Albright and I believe that immigrants who came to the US do not come to invade and to ruin, but to enrich it and to enrich themselves.
Another problem that is I have with Lionel Shriver is that she is presenting an incomplete and bias picture of the way the world views the United States. The US is envied by the world because it is one of the best countries that there is at integrating its immigrants in its society. Very few countries in the world can argue that immigrants and their children are able to participate and to even have great roles and great jobs in their societies.
France, for example, has an integration problem and so do most European countries. The main reason why there was unrest in the banlieues (the suburbs) of French big cities was that France hasn't make enough effort to integrate immigrants, their children and their grandchildren who are now French into the society. It has instead marginalized by pushing them away from big cities where unemployment and insecurity are commonplace. Thus, the suburbs of France were burning last Fall because France on the contrary to the United States hasn't succeeded in making its immigrants and their descendants feel fully French by giving them the most important benefit that comes with citizenship and that is the right to expect the State and elected officials to improve your life.
Thus, the American "integration" machine is working better than the ones of other countries. Lionel Shriver could have argued for a better enforcement of US immigration without trying to make a thoughtful but erroneous point about the United States, which isn't a victim, but rather a country in transition, which is trying to figure out what it wants to be.
Many Americans were fine with their country being a nation of immigrants as long as these strangers looked and had the same culture than them. Now that most immigrants are no longer Europeans and the United States is becoming a real melting pot in the sense that it is becoming less and less "white", many are talking about an "immigration" crisis and about the fact that America is under siege and will stop to be Western if something isn't done.
Lawrence Downes makes strong points in his op-ed in the New York Times, which rebuts Lionel Shriver's arguments:

[...] it's foolish to think that walling off America and reforming immigration through enforcement alone is anything but self-defeating. It's not only because the costs of security are so high, or because the contributions that legal and illegal immigrants make to this country are so positive. Those who have been working as hard as the hard-liners have been to close this country off to people who came here to seek work and a future have a radically astringent vision of what this country should be. To militarize the border, to turn illegal immigrants into felons, means trying to reverse the polarity on the American magnet, to repel the people who have struggled, dreamed and died to get here. It means turning this singular country into just another industrial power with a declining birthrate and a self-defeating antagonism to the foreign born. It means defining down what America stands for, no matter what the cost to the American economy, its traditions and values and moral standing. It's dangerous. It's not rational. But the argument on the restrictionist side isn't about being rational. It's about being afraid.