A stated (often fabricated) time pressure — implying the approacher has to leave soon — used to lower the perceived commitment cost of an interaction for the other person. Framed as a general-purpose softening tool, not a one-time opener line: it's reusable any moment the target is "leaning out" or half-stopping mid-conversation, not just at the open.
Mechanism: attention feels like a bigger ask when it implies an open-ended commitment ("talk to this stranger indefinitely"). Bounding it explicitly ("I have to go in a minute, but...") converts the ask into something small and safe to grant.
Where it fits: the false time constraint is deployed inside the The Opening Sequence (Angle → Pre-Open → Eye Contact → Pauses → Follow-Up) — after the Pre-Open and opening line, and again at any later point where engagement is flagging. It serves the same underlying goal as Leading With an Off-Ramp — reducing perceived commitment to make engagement lower-risk — but works from the approacher's side (bounding his own presence) rather than the target's.
Part of a broader staged model where each phase buys progressively more time — seconds at the open, a minute after the follow-up, five minutes of real conversation, then hours — with attraction compounding at each stage. See Momentum Management in Graduated Escalation for the escalation structure this feeds into.