Few-shot object detection (FSOD) is an emerging problem aimed at detecting novel concepts from few exemplars. Existing approaches to FSOD assume abundant base labels to adapt to novel objects. This paper studies the task of semi-supervised FSOD by considering a realistic scenario in which both base and novel labels are simultaneously scarce. We explore the utility of unlabeled data and discover its remarkable ability to boost semi-supervised FSOD by way of region proposals. Motivated by this finding, we introduce SoftER Teacher, a robust detector combining pseudo-labeling with representation learning on region proposals, to harness unlabeled data for improved FSOD without relying on abundant labels. Extensive experiments show that SoftER Teacher surpasses the novel performance of a strong supervised detector using only 10% of required base labels, without experiencing catastrophic forgetting observed in prior approaches. Our work also sheds light on a potential relationship between semi-supervised and few-shot detection suggesting that a stronger semi-supervised detector leads to a more effective few-shot detector.