It's possible, according to PerSquareMile, a blog dedicated to the issue of human density. Turns out if the whole world was as densely packed as New York City, everyone would theoretically fit into an area the size of Texas. We can certainly imagine a few practical obstacles (i.e. housing, energy, food production, and manufacturing) but the idea of multicultural neighborhoods being the norm does sound appealing.
HotPads recently moved offices into the Mission District of San Francisco, so we can definitely appreciate the diversity of people, cultures, and food within a several block radius. Also, since we already have a HotPads branded car cruising the streets of Dallas, we're pretty much set for the future Texas megalopolis.