Small amplitude oscillatory shear rheology is employed in order to investigate the linear viscoelastic behavior of the lower critical solution temperature blend polystyrene/poly(vinyl methyl ether), PS/PVME, as a function of temperature and composition. At low temperatures, where the mixture is homogeneous, the dependence of the zero shear viscosity (eta(0)) on concentration is measured and is well-described by means of a new mixing rule, based on surface fractions instead of volume fractions. Shift factors from time-temperature superposition (TTS) exhibit a Williams-Landel-Ferry (WLF) behavior. As the macrophase separation temperature is approached (the phase diagram being established by turbidity measurements), the blend exhibits a thermorheologically complex behavior. A failure of TTS is observed at low frequencies, both in the homogeneous pretransitional and in the two-phase regimes. Its origin is attributed to the enhanced concentration fluctuations, which exhibit a critical slowing down near the phase boundary in the homogeneous regime, and in the two-phase morphology inside the phase-separated regime. The anomalous pretransitional behavior can be quantified using a recent mean field theory, yielding the spinodal temperature. Furthermore, in the two-phase region an intermediate region of enhanced moduli at low frequencies is observed, followed by flow at even lower frequencies, which is attributed to the two-phase structure. The linear viscoelastic properties of the phase-separated blends are, to a first approximation, adequately described by a simple incompressible emulsion model considering a suspension of droplets of one coexisting phase in the matrix of the other phase.