I belive there is a woodruff key on the impeller shaft. It probably sheared. The setscrew isn't designed to take force.

The auger and impeller assembly needs to removed from the bucket, then the impeller comes off, then you can get to the key.

Is removing it and putting it back an easy job for a novice or should I bring it somewhere?

Assuming nothing's rusted up it's not a job that requires special skills, but it is rather time consuming.