Hi zedoul,
There is no formal upper limit. However, keep in mind that you might run into identifiability issues if the number of regressors is too large compared to the number of observations. For example, if you have tens of observations but hundreds or thousands of potential predictor variables, you might consider reducing the dimensionality of the predictor variables first, e.g., using a PCA. Generally, though, the spike-and-slab prior that's part of CausalImpact (through bsts) performs very well in identifying the relevant subset of predictors.
Kay