Condition: the phrase must have been coined for the song.
It cannot be a pre-existing expression that has become more widespread through song.
One recent episode of NPR’s Wait, Wait … Don’t Tell Me (with which I’m a little besotted) had a segment entitled:
It’s Not Easy Having Green
Now, I’m well aware that everyone who writes for Wait, Wait knows about the song, and that every NPR listener probably knows about the song, but my point is that, if you didn’t know about the song, you might be forgiven for thinking the phrase was a proverb or something.