Here are my thoughts:
There are two kinds of deadlines: real deadlines and false deadlines.
Real deadlines involve money. For example, you're working on a mix for a TV spot where the air time is already purchased. Or you're working on a mix for a film that is already booked in a festival. Or you're doing voice production or sound design for a game that has a hard ship date.
Generally, when people have already spent money and made commitments for things that happen after your step in the production process then you're up against a real hard deadline.
If you're part of an audio production team like in a film, then your short term and long term deadlines affect every other member of the post production team.
If you have either left the studio or slept in the days leading up to a hard deadline and you miss that deadline then you've made a huge error that will have significant impact on your career and business.
Even if you haven't slept or left the office you've made the same error, but your wrongdoing is more on the front end of the project than the back.
If you find yourself in a situation where you're up against a hard deadline that you can tell you won't be able to meet, then you have to call in help. Break the project into a couple of pieces and outsource them to get it done. Even if it costs you money in the short term, it'll cost you less over time.
Really, the rule of thumb is to never miss a hard deadline.
The other types of deadlines are false deadlines. False deadlines are still good to hit, but the consequences are far less dire.
False deadlines are when the client would like to the audio mix by tomorrow so that he can have a few days of buffer before he has to send it out on his hard deadline. Or when you ask for a deadline and the client really doesn't have one at all, so he just spits out an unrealistic date because he doesn't know what it takes to make his works sound good.
False deadlines are negotiable, but they must be negotiated explicitly and well in advance of the deadline passing by. Also, no one calls them false deadlines, and you shouldn't either. Just try to find out exactly what happens once you deliver the audio, and you'll get a sense of how real your deadline is.