People always like to think they're living in the most important time.

"This is the most important election of our lifetime......until the next election"

The only time the phrase "America is over" was relevant was the time surrounding the Civil War. At that time, the entire concept of America was in limbo.

To answer your question more directly, I think people are referring to your first definition when they say something like that.
But it doesn't make sense. The idea of America isn't static. America is different now compared to 1776. So did America end somewhere inbetween?