I am an American and I'm happy to have been born in a country that guarantees basic rights and freedoms. I'm proud that we have a history of forging a path of our own and that, though we've made tons of mistakes and committed atrocities along the way, we were willing to learn and change. I'm happy that I can go to church, marry any guy over the age of consent (and any girl, depending on some states), have whatever job and not be killed or oppressed in any way for it. While we still have plenty of issues we need to work on, I'm glad I was born here.
However, I do consider myself a global citizen. When Jesus told everyone to love their neighbor, He was asked who neighbors were. This prompted Him to tell the story of the Good Samaritan. For those that don't know, the story involves a man who had gotten injured in an accident. The supposed holy ones of the Jewish community at the time walked by but did not notice him. It was a Samaritan, a foreigner despised by the Jewish people, who ended up helping the man. Jesus used this story to say that the definition of "neighbor" goes beyond kin or tribe. Thus, as a Christian, I feel I'm called to serve my neighbor, whether that neighbor is Kenyan, American, Pakistani, or Mexican. Wherever I end up, I should serve. That's where I say the call of my faith ranks higher than my citizenship.
In addition, serving the world helps America, whether America realizes it or not. We are interconnected for good or for ill, whether we're depending on China for economics or Saudi Arabia for oil. By helping others gain their rights and stand on their own feet, we are creating potential allies. Likewise, negative actions (such as deposing of elected leaders and supporting dictators) have negative consequences for us throughout the world. Like most species, human beings are an interdependent group. As people need each other, so do countries.
Loving my country means keeping it accountable. It means encouraging it to participate with everyone else (everyone likes friends, right?). It means expanding tis horizons and helping it to be the best it can be. We'd encourage this of individual people. As an economics professor of mine once said, countries are collections of people. Wouldn't these rules still apply?