There's nothing special about tge phrase "American mouth," it just means the mouth belongs to someone that is American. Your right that the pill most like symbolizes something unpleasant. The fact that he uses the adjective "American" most likely means that which the pill represents is something that might be unpalatable to American sensibilities. The lyrics reference Christ, and Christianity played a large role in shaping American culture, so it may be something that might upset a Christian's sensibilities.

The song takes several strong images, and strings them together in a fairly obscure way. People can interpret it in very different ways, and it probably wasn't intended to tell a single story. So, I'll try to give you several possible options: you can decide which one seems most likely to you. American mouth, big pill looming 1. I am an American who is proud to exercise my free speech (through my mouth). Society is trying to silence me and sedate me, as if it were giving me psychiatric pills. 2. Like most other Americans, I always (use my mouth to) talk loudly about things I don't understand. I am about to learn some difficult lessons that will shake me out of this delusional overconfidence. Those lessons will be a bitter pill to swallow. 3. American culture is defined by consumerism. We aren't citizens we're consumers. We're giant mouths, and nothing else. 3A. All this consumerism is like a psychiatric drug that is sedating us. OR 3B. We are about to get a strong lesson that will take us away from the consumerism. OR 3C. One of the things we consume is illegal drugs. 4. There is a girl with a beautiful mouth, like a beauty queen in the "Miss America" pageant. Either she or her lover is about to get either a medical pill, or a psychiatric pill, or an illegal pill, or a metaphorical pill. 5. There is a talented singer, whose mouth makes songs that are a national treasure. However, the singer has psychiatric problems requiring medication; or is about to learn an important lesson; or is addicted to illegal drugs. This interpretation fits well with the "flightless bird" line: we expect birds to do two things: fly and sing. I'm sure there are other interpretations, but all of these seem plausible to me.