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.
Belgian artist Stromae brings an irresistible dance groove to a subject most party tracks completely ignore: the people working while everyone else has fun. Instead of toasting the partygoers, he raises his glass "À ceux qui n'en ont pas" [To those who don't have one], dedicating the beat to the staff behind the scenes. He shouts out Rosa who cleans up the mess ("quand on fout l'bordel, tu nettoies"), Albert who collects empty glasses, Céline dealing with coats at the cloakroom, and Arlette stuck working in the restrooms. He also takes hilarious, sharp jabs at obnoxious party guests, like the rude customer complaining that two drinks are taking three hours and threatening the waiter's job with "Appelle-moi ton responsable" [Call me your manager].
Stromae cleverly plays with French idioms on the dance floor. When he chants "tu pourras toujours te brosser", he relies on the slang meaning of se brosser (literally "to brush yourself"), which means "you can forget about it!" He then broadens his toast beyond the club to everyone on terrible shifts: nurses, bakers, truck drivers, flight attendants, and exhausted new parents soothed only by crying babies ("bercés par les pleurs"). It turns a classic club banger on its head by partying for the people who are simply too tired or busy to celebrate.