.....basically tacking towards the center
I think that this is exactly what Bernie Sanders is well positioned and motivated to prevent.
No one is to the left of Bernie Sanders , but Hillary Clinton is close , nearly as left in outlook, and needs to be, to keep her base from defecting to Bernie Sanders before the convention.
I would bet that she has a calendar date circled, on her master planning calendar, the day she makes a major turn clockwise and starts to appeal to the right and center. She has a speech made up for that day with words and phrases carefully crafted to mollify the right and capture the center.
If Bernie Sanders isn't really hoping to become president ,perhaps if you remember what a very committed leftist he is , there is a potential for him to get something he wants even more than he wants to be president . He can pull the entire campaign and political discussion far more to the left than the potential winner ever planned . This will very likely pull the opposition candidate left as well as the location of the center will change its definition.
If you can't be the leader , can you lead the leader?