I am not sure exactly what the smart start quiz is, but looking at the website it seems similar to the ILIP quiz of old.
The repercussions of not completing the quiz is that the library will withhold your final marks (same thing they will do to you if you fail to pay fines by the due date). They would, I assume, release your results once you finish the quiz, although it sometimes takes a while.
That being said, I can't find any reference to a due date for the quiz on the library site and I was able to start the quiz just then. Possibly the due date is set by the commerce faculty and your assignments from now will assume that you have completed the quiz, from memory ILIP used to contain questions on how to reference correctly and most likely Smart Start would too, so maybe from now on there are now excuses for not providing correct references in assignments or something else along those lines.
Though as I am not a commerce student, I am only guessing at the repercussions they have for not finishing the quiz and I would suggest (unless someone else here can say) you check with the people that set the due date you mentioned.