Magnetic resonance imaging (MRI) is an essential diagnostic tool that suffers from prolonged scan times. Reconstruction methods can alleviate this limitation by recovering clinically usable images from accelerated acquisitions. In particular, learning-based methods promise performance leaps by employing deep neural networks as data-driven priors. A powerful approach uses scan-specific (SS) priors that leverage information regarding the underlying physical signal model for reconstruction. SS priors are learned on each individual test scan without the need for a training dataset, albeit they suffer from computationally burdening inference with nonlinear networks. An alternative approach uses scan-general (SG) priors that instead leverage information regarding the latent features of MRI images for reconstruction. SG priors are frozen at test time for efficiency, albeit they require learning from a large training dataset. Here, we introduce a novel parallel-stream fusion model (PSFNet) that synergistically fuses SS and SG priors for performant MRI reconstruction in low-data regimes, while maintaining competitive inference times to SG methods. PSFNet implements its SG prior based on a nonlinear network, yet it forms its SS prior based on a linear network to maintain efficiency. A pervasive framework for combining multiple priors in MRI reconstruction is algorithmic unrolling that uses serially alternated projections, causing error propagation under low-data regimes. To alleviate error propagation, PSFNet combines its SS and SG priors via a novel parallel-stream architecture with learnable fusion parameters. Demonstrations are performed on multi-coil brain MRI for varying amounts of training data. PSFNet outperforms SG methods in low-data regimes, and surpasses SS methods with few tens of training samples. On average across tasks, PSFNet achieves 3.1 dB higher PSNR, 2.8% higher SSIM, and 0.3 × lower RMSE than baselines. Furthermore, in both supervised and unsupervised setups, PSFNet requires an order of magnitude lower samples compared to SG methods, and enables an order of magnitude faster inference compared to SS methods. Thus, the proposed model improves deep MRI reconstruction with elevated learning and computational efficiency.