There is no any specific word for sausage-maker. Колбасер does not, did not and never could mean it in common general Russian.
this -er ending in kolbaser is clearly mimicking English, so it is of latest after-Perestroika times. While "колбаса" word is much more old. If there would be a really Russian word for sausage-trader or sausage-craftsman it would probably be built with -nik suffix instead. Колбасник. Just like мясник (butcher, from мясо=meat), кукурузник (derogatory nickname for Khrushev for his policy of enforcing American corn in USSR). Or maybe -shchik like in старьевщик (collector/reseller of OLD things). Or -chik as in грузчик (load runner). But not -er. This is clearly a pattern from West.
there is a jargon verb колбаситься, literally to sausage oneself. It was referring some music parties, where lot of physical actions and heavily crowded rooms were over comfort and sound quality. Maybe it somehow relates to English "jamming" term. While "jamming" does not seem to imply getting squeezed as in "taffic jam".
Such kinds of dancing clubs, night loud music parties for youth, they are also western post-Perestroika influence. So it is natural that a person who does oneself (or maybe causes others to) start колбаситься, would be named by that new-made noun, build from this new-made verb using English -er pattern. Afterall everything American and European was very trendy in 1990-s. And West-style night dancings surely were focal points for wannabe-Westerners.
However, no matter what etymology of that verb is, it practically has no relation to the колбаса as food (sausage). Neither does "колбасер".
w.r.t. lyrics I only found this http://webkind.ru/text/94567214_5126008p995356038_text_pesni_nas-vstavlyaet-kolbasa.html
Мы колбасим до утра
Нас встaвляет колбаса.
Нас вставляет колбаса
Колба- колба- колбаса.
Скорость нас вставляет.
This heavily uses drug addicts and dancing addicts slang, so I would hardly make good translation of it. but there is also nothing to translate. They in different forms convey how they like to колбаситься faster and faster
In particular, "колбаса" here is retrofitted from the said slang verb, meaning here the process when many people are "sausaging" themselves.
"Вставляет" probably means "rushing" as in "....the feeling you get on smoke when the top of your neck feels like it's going into the back of your head.", see pp.109/110 at Gift of Wings