The secret to asking for a deadline extension is to make it clear that your only problem is time; nothing else is wrong. Rather than coming in to your supervisor with an apology and series of reasons why you're not going to be able to meet the established deadline steer the discussion as quickly as possible to solutions. The schedule established was clearly unworkable, and now you need help in coming up with ways to deal with the situation. Offer alternatives but make it clear that delivery as intended is impossible.
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