The Schwinger variational principle is applied to electron-hydrogen scattering in the zero-angular-momentum model, and it is shown that when the wavefunction is represented on a basis of target states (or pseudostates) this procedure offers a tractable and economical method of calculation. Attempts to remove the pseudoresonances associated with the expansion of the wavefunction in target pseudostates by modification of the Green function in the Schwinger functional were partly frustrated by the occurrence of singularities associated with the variational method itself.