Large Language Models (LLMs) generate text token-by-token in discrete time, yet real-world communication, from therapy sessions to business negotiations, critically depends on continuous time constraints. We use simulated negotiations between paired agents under strict deadlines to study adaptation to real-time pressure. Agents either receive only the initial deadline or explicit remaining-time updates at each turn. Remaining-time feedback raises deal closure from 4% to 32% for GPT-5.1-chat-latest and increases offer acceptance more than sixfold. The same model achieves near-perfect closure under turn-based limits, showing that poor wall-clock performance is not simply due to insufficient negotiation competence. Across additional interface conditions, qualitative urgency cues can outperform numeric countdowns, repeated deadline reminders do not consistently reproduce their benefits, and directed time tracking can help or hurt depending on the model. Across additional negotiation scenarios and model configurations, we find real-time temporal adaptation is fragile, model-dependent, and sensitive to how temporal constraints are presented. Code available at https://github.com/sehgal-neil/llm-temporal-awareness

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