The R command `cov2cor(vcov(fitted_model))` will return you the covariance matrix of regression estimates. It is [proportional][1] to $(X'X)^{-1}$, which means that in the extreme case of a perfect correlation of a slope and an intercept the covariance matrix is rank deficient. Hence, rank deficient is the matrix $X'X$, which is a definition of [perfect multicollinearity (PM)][2]. PM can be problematic for inference, but often is no big deal for forecasting


  [1]: https://en.wikipedia.org/wiki/Ordinary_least_squares#Finite_sample_properties
  [2]: https://en.wikipedia.org/wiki/Multicollinearity