There is a need for fast adaptation in spike sorting algorithms to implement brain-machine interface (BMIs) in different applications. Learning and adapting the functionality of the sorting process in real-time can significantly improve the performance. However, deep neural networks (DNNs) depend on large amounts of data for training models and their performance sustainability decreases when data is limited. Inspired by meta-learning, this paper proposes a few-shot spike sorting (FS-SS) framework with variable network model size that requires minimal learning training and supervision. The framework is not only compatible with few-shot adaptations, but also it uses attention mechanism and dilated convolutional neural networks. This allows scaling the network parameters to learn the important features of spike signals and to quickly generalize the learning ability to new spike waveforms in recording channels after few observations. The FS-SS was evaluated by using freely accessible datasets, also compared with the other state-of-the-art algorithms. The average classification accuracy of the proposed method is 99.28%, which shows extreme robustness to background noise and similarity of the spike waveforms. When the number of training samples is reduced by 90%, the parameter scale is reduced by 68.2%, while the accuracy only decreased by 0.55%. The paper also visualizes the model's attention distribution under spike sorting tasks of different difficulty levels. The attention distribution results show that the proposed model has clear interpretability and high robustness.