Unrolled neural networks (UNNs) have surpassed state-of-the-art methods for dynamic MR image reconstruction from undersampled k-space measurements. However, 3D UNNs suffer from high computational complexity and memory demands, which limit applicability to large-scale reconstruction problems. Previously, subspace learning methods have leveraged low-rank tensor models to reduce their memory footprint by reconstructing simpler spatial and temporal basis functions. Here, a deep subspace learning reconstruction (DSLR) framework is proposed to learn iterative procedures for estimating these basis functions. As proof of concept, we train DSLR to reconstruct undersampled cardiac cine data with 5X faster reconstruction time than a standard 3D UNN.