At first, I was totally thrown off by the fact passe could ever mean descendant, which I expressed (using different words) in a comment under the original post. Then I listened to the song, after reading what people mentioned on the discussion linked. And at some point during the second chorus, the puzzle magically solved itself and everything started to make sense. Though this is by no mean a final or definitive explanation, here are a few of my reflections on the verse.
But first things first: Daniel (or whoever he is impersonating in the song, though it appears it would be him, since he uses the real name of his father) is an artist who enjoys playing music. He plays it for free and for money, for fun and for a job, seriously and frivolously, during the day and at night, for his friends, for total strangers and even for himself only, as evidenced by ‘j'ai chanté tout nu dans mon bain’. As of recently, Luke pointed it out in a comment below, he further widened his public by playing for the dead.
He is now on the stage and someone is eager to get him going, so that the crowd is entertained and the rotten tomatoes are kept away from the stage. This person is talking to Daniel in the chorus ‘Brasse, brasse la passe à Thanase / Fini mon numéro / J’veux pas d’tomates / ...’. This is where we need to find out what la passe à Thanase mean.
In most societies, one might be refered to as the son or daughter of one of their parents. Icelandics actually carries that denomination their whole life as a part of their legal name. From saying ‘Daniel, fils d’Athanase’, we can easily get to a simpler ‘le fils d’Athanase’. Most French-Canadians will gladly go from there to ‘le fils à Athanase’, with no more than a slight remorse for being a little cavalier with the beau-parler.
This question, instigated after the first few comments under the initial post, tries to answer the origin of this familiar tour de langue.
From here, things get a little crude. A child is the product of a sexual intercourse between a man and a woman, and the man always had his pleasure in the conception. A passe is a rather vulgar word for the said sexual intercourse, not necessarily involving any type of love, nor desire or even consent from the lady’s part. Calling a child by the name of the process at the very beginning of the human existence is rather disrespectful at best (in league with ‘son of a bitch’). Using such a harsh word as passe to refer to it is right-down insulting. But since it is here self-directed, one may decide it’s ok, though in the song, it is not really self-directed: Daniel is singing words that were thrown at him at some point.
So my guess is that whoever is addressing Daniel like this is in such a position of power that being this mean only has minimal consequences. This indicates that Daniel’s life ain’t easy and that though he may have high hopes for the future, he’s currently accepting to be badly bullied because there’s no way around it for now.