Origin of species
It suggests to me a form of validation, suggesting that being American alone is insufficient. Being able to trace your ancestors back to another country may well make for interesting genealogy, but with each successive generation the individual culture brought over all those years ago is distilled, to the extent that any pretence of being from Greece, for instance, gradually becomes a mockery, one dependent upon the very basics. The limited availability of Greek foods, to take one example, leaves the self-proclaimed Greek-American family clutching at straws, taking the little they can find, with the result that the original culture boils down into stereotypes. It's said that none are so English as the English abroad, usually with reference to holidaymakers, but it applies equally to emigrants.
Somewhere along the line, I suspect, the pride with which the immigrant boasted his origins - "America's my adopted home but I'm from Ireland", that sort of thing - turns into a formulaic expression, so that some years down the line, it's bereft of any power. I recall hearing about Matt LeBlanc complaining, when required to keep a trim figure for Joey, that "I'm Italian and in my thirties". I'm sorry, that's not fooling anyone: we all struggle to keep our weight down, so by this stage, it's become little more an excuse.
That said, the worst of it has been, predictably enough, on the internet, a place where shorthand is rife. Confusion abounds when, in a chatroom, I greet someone who tells me they're German with the words "wie geht's?' and they don't understand a word of it, and don't get me on to the person from Jersey who'd not even heard of the Channel Islands ...
Don't get me wrong here: I'm not saying that any attempt to maintain so much as a semblance of another culture in America is a sham: it's just inevitable that in a melting-pot society, the finer points of what makes up a specific culture do tend to get lost.
To finish on a more positive note, I wonder if a subconscious desire for liberal America to place a distance between themselves and the country as a whole hasn't come into the equation, as a means of showing that the America is not united behind Bush. This system of dual cultures is not so recent as to have evolved from the current political climate, but it'd be heartening to think it's resulted in increased cultural awareness.