We study the structure and thermodynamics of the critical nuclei in metastable binary polymer blends using the self-consistent field method. At the mean-field level, our results are valid throughout the entire metastable region and provide a smooth crossover from the classical capillary-theory predictions near the coexistence curve to the density functional predictions of Cahn and Hilliard (properly transcribed into expressions involving the parameters of the binary polymer blends) near the spinodal. An estimate of the free energy barrier provides a quantitative criterion (the Ginzburg criterion) for the validity of the (mean-field) self-consistent approach. The region where mean-field theory is valid and where there can be a measurable nucleation rate is shown to be poorly described by the existing limiting theories; our predictions are therefore most relevant in this region. We discuss our results in connection with recent experimental observations by Balsara and co-workers.