From changing fashion trends to views on world leaders and economic policies, large-scale shifts in group positions happen regularly and unexpectedly. How can we track these in the wild? How can we characterize them? Existing work has primarily leveraged stance detection to track shifts of specific groups on a single issue. However, such methods will only find shifts when they accurately pick exactly the right group and right issue. They do not capture the multi-dimensional, multi-resolution stance landscape in which these shifts actually happen. To better model drift and shift in public opinion, we require a framework that can track change at the population level, across a diverse range of issues. We propose a method to infer the potential landscape of stance dynamics, the gradient of which shows large-scale stance shifts, and apply it to show en-mass stance shifts by prominent Canadian political figures across multiple platforms and years. We do this using large-scale stance detection to find stance expressions, dimensionality reduction to find the low-dimensional linear latent space, and potential landscape neural networks to find the potential landscape of that space. This allows us to find a coherent, linear, three-dimensional space that explains 45\% of the variance in stance, where we can explain the specific characteristics of each dimension. We show that while the predictive performance is sufficient to validate its descriptive-ness, in practice its predictive performance is mixed.