Large language models have improved argument mining substantially, but the associated computational cost complicates deployment, replication, and systematic comparison. We examine how much compression an open-source large language model can tolerate before argument classification quality degrades. Using gpt-oss-20b as the base model, we study pruning with Wanda and post-training quantization under a zero-shot prompting setup. We evaluate compressed variants on three argument-mining resources, namely UKP, Args.me, and ARIES, and contrast their behavior with general language-model benchmarks. The results show a consistent pattern: moderate pruning preserves most of the original performance on argument classification, whereas activation quantization causes larger and more systematic drops. The findings suggest that argument classification is more compression-tolerant than general-purpose evaluation suites, but only up to a point, and they should not be interpreted as evidence that aggressive compression is universally safe. We therefore position compression as a practical way to reduce model cost for argument analysis, while emphasizing that claims about efficiency gains must distinguish between preserved predictive quality and realized runtime speedups.