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Gibbs ensemble Monte Carlo simulations were run with an efficient mixed-basis electronic structure method to explore the phase equilibria of water from first principles using Kohn-Sham density functional theory. The Perdew-Burke-Ernzerhof exchange/correlation density functional gives a higher critical temperature (700 K) and boiling point (480 K) than experiment, although good agreement is found for the saturated liquid densities. A systematic increase in the size of the basis set for the Becke-Lee-Yang-Parr exchange/correlation density functional from a double-ζ to quadruple-ζ split valence leads to further deviations from experiment on the saturated liquid and vapor densities, while the intermediate basis set gives the best results for the heat of vaporization at T = 423 K. Analysis of the liquid structure for all simulations shows changes that can partially be explained by the different densities at a given temperature, and both density functionals show a similar temperature dependence of the liquid structure. [ABSTRACT FROM AUTHOR]