Supervised keypoint localization methods rely on large manually labeled image datasets, where objects can deform, articulate, or occlude. However, creating such large keypoint labels is time-consuming and costly, and is often error-prone due to inconsistent labeling. Thus, we desire an approach that can learn keypoint localization with fewer yet consistently annotated images. To this end, we present a novel formulation that learns to localize semantically consistent keypoint definitions, even for occluded regions, for varying object categories. We use a few user-labeled 2D images as input examples, which are extended via self-supervision using a larger unlabeled dataset. Unlike unsupervised methods, the few-shot images act as semantic shape constraints for object localization. Furthermore, we introduce 3D geometry-aware constraints to uplift keypoints, achieving more accurate 2D localization. Our general-purpose formulation paves the way for semantically conditioned generative modeling and attains competitive or state-of-the-art accuracy on several datasets, including human faces, eyes, animals, cars, and never-before-seen mouth interior (teeth) localization tasks, not attempted by the previous few-shot methods. Project page: https://xingzhehe.github.io/FewShot3DKP/