A variational principle is not generally satisfied in steady-state quantum transport as opposed to the case of ground-state problems. We show that for a short-range potential, a functional for the scattering amplitude can be introduced that is stationary for arbitrary variations about the exact scattering wave function. However, except for the special case of spherically symmetric potentials, the functional does not satisfy any minimum principle even in linear response and for single-channel scattering. The absence of a minimum principle puts severe limitations on the choice of trial wave functions in transport calculations. Examples of electronic transport in selected quantum wires will be presented to illustrate the problem.