Poulos: "the world is not a polity, so citizenship in it is impossible." Far be it from me to defend Barack Obama, but I'm positive that's not what he meant; he's playing with a notion of identity wherein one has symbolic but meaningful ties to the rest of the world, which are not reducible to the kinds of relationship that come from national identity, but are in some way analogous to it. Like every analogy, it runs in a certain area, but cannot cover all possible implications of meaning, especially literal ones. The underlying philosophical position is common: lots of people try to explain how one can have attachments to place as well as attachments beyond it. Charles Taylor's been on the brain lately, so one could think about this as analogous to the historical conversation of all Christians across the millennia--I have attachments to people who are close to me (the other members of my church) and people who are far away (Augustine, Luther, etc). Neither identity or attachment threatens the other. There may be some cosmopolitans who argue that all identity ought to be effaced, but I'd be hard pressed to name a non-utilitarian who holds that position, and I am quite certain Obama did not mean that.
While its modern usage often suggests an affinity for or loyalty to other places besides or even in addition to one’s own community, the word came into being to define the repudiation of political and social bonds. To trace kosmopolitis back to its origins is to trace it to those who believed all forms of social and political obligation to be worthless, which is often the opposite of what people who fancy themselves “cosmopolitan” actually support. In fact, the broad and universal sort of character that acknowledges and respects the diversity of the world that people think has something to do with cosmopolitanism is more appropriately defined by such words as ecumenical or catholic. Strangely, though perhaps not so surprisingly, those who identify with some form of cosmopolitanism tend to be the same people who would like to see the world’s political and cultural diversity reduced to a monoculture of managed democratic capitalism, which confirms that there is something essentially intolerant and destructive of established cultures and traditions in the cosmopolitan view. The phrase is meaningless, but the idea that the phrase hints at is quite undesirable.
I'd be surprised if anyone who subscribes to the modern, English-language meaning of 'cosmopolitan' would be willing to follow Larison back to the Greek roots of the term. Words change their meanings all the time. I'm sure you could tell a (long) historical story about how we got from that old use to the current one, but I don't know that it illuminates anything about what current cosmopolitans believe, any more than picking some political belief and finding some unsavory person who advocated it compromises the viability of that belief now. As Larison hints, there's a difference between cosmopolitanism and universalism (though he seems to conflate the two), but cosmopolitanism does have a meaning: the one that he's just spent a paragraph outlining.