Being the right kind of demanding as a college instructor
If people have a legitimate reason for wanting an extension of the deadline, I would simply give them the extension. If they cannot provide a good reason, i.e. they simply procrastinated too much, they have to take responsibility for their behavior, and they do not get the extension. 

This has nothing to do with being a hard-ass, but being fair. Other people have done the work, and giving people that procrastinated an extension is not fair to them. In addition, getting work done that you where assigned (even if it is hard or boring) is a valuable lesson to teach a student. Their future boss will also not be sensitive to a missed deadline because of procrastination.