Recent work has demonstrated the remarkable potential of Large Language Models (LLMs) in test-time scaling. By making models think before answering, they are able to achieve much higher accuracy with extra inference computation.However, in many real-world scenarios, models are used under time constraints, where an answer should be given within a certain output length. It is unclear whether and how the reasoning ability of different LLMs remain effective under strict constraints.We take a first look at this problem by conducting an in-depth empirical study. Specifically, we test 30 LLMs on common reasoning datasets under a wide range of output length budgets, and we analyze the correlation between the inference accuracy and various properties including model type, model size, prompt style, etc. We also consider the mappings between token budgets and actual on-device latency budgets.The results have demonstrated several interesting findings regarding the budget-aware LLM reasoning ability that differ from the unconstrained situation, e.g. the optimal choices of either model size or prompt style change under different budgets. These findings offer timely evaluation to this area and practical guidance for users to deploy LLMs under real-world latency constraints.