Summarizing a document within an allocated budget while maintaining its major concepts is a challenging task. If the budget can take any arbitrary value and not known beforehand, it becomes even more difficult. Most of the existing methods for abstractive summarization, including state-of-the-art neural networks are data intensive. If the number of available training samples becomes limited, they fail to construct high-quality summaries. We propose MLS, an end-to-end framework to generate abstractive summaries with limited training data at arbitrary compression budgets. MLS employs a pair of supervised sequence-to-sequence networks. The first network called the \textit{MFS-Net} constructs a minimal feasible summary by identifying the key concepts of the input document. The second network called the Pointer-Magnifier then generates the final summary from the minimal feasible summary by leveraging an interpretable multi-headed attention model. Experiments on two cross-domain datasets show that MLS outperforms baseline methods over a range of success metrics including ROUGE and METEOR. We observed an improvement of approximately 4% in both metrics over the state-of-art convolutional network at lower budgets. Results from a human evaluation study also establish the effectiveness of MLS in generating complete coherent summaries at arbitrary compression budgets.