The main obstacle to getting people to think of themselves as global citizens is the feeling of nationalism. Nationalism can be defined as pride in and identification with one's own country, ethnic group, and/or religion. In other words, nationalism is the desire to categorize the world into "self" and "other."
As Thomas Friedman points out in The Lexus and the Olive Tree, the globalization that has changed our world has not destroyed the inclination towards nationalism. Instead, people continue to think of themselves in parochial ways where they side with their own kind against people they see as enemies. As long as this sort of attitude persists (and it seems to be very resilient), it will be very hard to get the majority of people to think of themselves as global citizens. Instead, they will continue to identify with their own country (or other grouping) and feel animosity towards its rivals.