The thing is, it’s right out there in current music. Older music is more likely to be full of innuendos.
I always got the impression that his SO left him for someone else, and he was going to punch out the someone else. 
I don’t think this would fly nowadays either. Might explain the propensity for domestic violence and/or why she left, too.
Perhaps you didn’t listen closely to the lyrics. The screech before the outro is:
[QUOTE=Doc Corbin Dart]
I WANNA TAKE THE PRESIDENT,
CHOP OFF HIS HEAD,
AND MAIL IT TO THEM IN A GARBAGE BAG!!!
[/QUOTE]
Now, violence in song is not unusual, but directing that violence at the President is. It’s especially unusual since the Titular would-be assassin had acted against the sitting President at the time. Yet Doc didn’t get even a phone call from the Secret Service. I’ve seen it speculated if he had used ‘am gonna’ instead of ‘wanna’, they might have discussed it with him.
Either way, calls to assassinate the President are rare in music.