Let \kappa_B be the least cardinal for which the Baire category theorem fails for the real line \mathbf{R}. Thus \kappa_B is the least \kappa such that the real line can be covered by \kappa many nowhere dense sets. It is shown that \kappa_B cannot have countable cofinality. On the other hand it is consistent that the corresponding cardinal for 2^{\omega_1} be \aleph_\omega. Similar questions are considered for the ideal of measure zero sets, other \omega_1 saturated ideals, and the ideal of zero-dimensional subsets of \mathbf{R}^{\omega_1}.