Temporal Action Localization (TAL) involves localizing and classifying action snippets in an untrimmed video. The emergence of large video foundation models has led RGB-only video backbones to outperform previous methods needing both RGB and optical flow modalities. Leveraging these large models is often limited to training only the TAL head due to the prohibitively large GPU memory required to adapt the video backbone for TAL. To overcome this limitation, we introduce LoSA, the first memory-and-parameter-efficient backbone adapter designed specifically for TAL to handle untrimmed videos. LoSA specializes for TAL by introducing Long-Short-range Adapters that adapt the intermediate layers of the video backbone over different temporal ranges. These adapters run parallel to the video backbone to significantly reduce memory footprint. LoSA also includes Long-Short-range Fusion that strategically combines the output of these adapters from the video backbone layers to enhance the video features provided to the TAL head. Experiments show that LoSA significantly outperforms all existing methods on standard TAL benchmarks, THUMOS-14 and ActivityNet-v1.3, by scaling end-to-end backbone adaptation to billion-parameter-plus models like VideoMAEv2~(ViT-g) and leveraging them beyond head-only transfer learning.