There are two things that happen when you miss deadlines, the first obvious, the second insidious.
The direct impact is that you don’t ship your product. Revenues come in later. Business partners are disappointed. Your team is let down.
The insidious part is that – drip, drip, drip – what you mean by “deadline” starts to erode. “Deadline” becomes “what we’re shooting for if nothing goes wrong.” But of course something always goes wrong, so the first sign of trouble becomes a chance to negotiate (with your team , with your business partners, and with your procrastinating self), a chance to argue that something’s got to give.
When hitting deadlines becomes non-negotiable, you and your team put that whole negotiation aside and just get to work. It’s amazing to discover what you can produce when you expect yourself to deliver every time.
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(If you’re curious: it turns out that the source of the word is a “dead line” for American Civil War prisoners who were kept inside a stockade. A railing placed inside the stockade marked the line prisoners were not allowed to pass – and guards were told to shoot any prisoner who crossed the line, because they were deemed to be trying to escape.)