Brosser literally means "to brush". However, in this song, Stromae uses the popular idiomatic expression "tu pourras toujours te brosser".
This is a sassy, colloquial way to tell someone "you can forget about it!" or "dream on!". It's used here as a warning to those who disrespect the everyday workers the song celebrates, telling them they won't get what they want without showing respect.
Ever been to a party and not even noticed the people cleaning up or collecting empty glasses? Stromae sees them. "Santé" is French for "Cheers!", but this dance track isn't a toast to the people having fun. It's a celebration for everyone else.
He starts by shouting out the workers by name: "Rosa, Rosa, quand on fout l'bordel, tu nettoies" (Rosa, Rosa, when we make a mess, you clean it up) and "Arlette, arrête, toi, la fête, tu la passes aux toilettes" (Arlette, stop, you spend the party in the toilets). He even includes a verse of rude things customers say, like "Appelle-moi ton responsable et fais vite" (Call your manager and be quick about it). The song then expands to toast all kinds of people who can't celebrate, from pilots and nurses—the "champions des pires horaires" (champions of the worst hours)—to new parents and anyone with a broken heart. It's a powerful and catchy way to ask us to raise a glass for those who can't.