The cold war "the American Way" versus "Communism" is now what many people think of when they hear the cliche. If you read that wiki page, you will notice the satire of the Simpson's song. It is often used in satire to make fun of people who would be the self righteous in America who pontificated against Communism during the cold war.
It was also what the founders of the multi-level marketing scheme Amway based the name of the business.
See... now when you can also connect it to the meaning of many of Woody Guthrie's songs about the lives of Americans (This Land Is Your Land... etc.) you can see that the meaning of the phrase is all in the intent of who is using it.

Mostly I think it is now seen as a phrase to satire self-righteousness.