Recent experiments by Balsara and co-workers have used neutron scattering to study quenches of binary blends of homopolymers from the one phase to the two phase region of the phase diagram. The size of the critical nucleus is extracted from the data as a function of quench depth into the two phase region. To help understand these observations, we coarse grain the polymer blend into an Ising model with nearest neighbor interactions and use Kawasaki spin exchange dynamics that fix the fraction of up spins at 10%. The time dependent structure factor is calculated along quenching trajectories, and we find qualitative agreement with the experimental observations of the critical nucleus. In particular, the critical size does not diverge as one approaches the mean-field spinodal in contradiction with the predictions of Cahn-Hilliard theory. Moreover, the calculation of the distribution of cluster sizes of up spins along the quenching trajectories reveals a qualitative picture in which multiple domains rich in up spins appear in a vast sea of mostly down spins.