Can you delay the due date for the game you are making?

You should always turn in code and software that is both functional and complete. That is your job as a professional software engineer, such as when you are paid to be a game developer, and should be your general rule of thumb while you are in school (high school, college, etc).

Good software is only late until its finished, bad software is released poorly and will be a pain to maintain forever and a nightmare to try to make good once people are using the product.

That said things happen as a students (and even as a pro) so things do come in late, so do not feel terrible!

As for your particular situation with high school I would try to contact your teacher (or who ever is going to grade this assignment) and let them know its going to be unfinished or late as soon as possible. They can decide if they would rather have an unfinished assignment to grade or let you turn it in late.

In my experience in college professors were usually reasonable and would accept assignments late. However they usually, but not always, applied some penalty for being late. An example would be docking a letter grade but letting you turn it in a week late (that is, once the assignment is turned in and graded if you were going to get an A the grade would be drop it down to a B).

In the professional setting, delaying the due date of a game does occur, but it is definitely not something you want to make a habit of. During the course of a gaming project there are often milestones or checkpoints that are used to make sure the game's development is on schedule. If at one of these milestones the game seems to be behind schedule, future milestones, like the release date may get "delayed" or pushed back.

Delays in development are often expensive though and often times it is better to "cut" or remove features then to not have the project completed on time. Delaying the due date is also frustrating to the people waiting to enjoy your product.

Just think of how you would feel if you were excited to get a game, movie or cd the day it was scheduled to come out only to find out the release date has been pushed back due to delays.

I don't have a great answer, it really depends on the circumstances. In 10 years of working in software at various companies I've seen most projects NOT completed in the original timeline. However, in high school and college most software projects had a strict due date, only a few exceptions when professors realized there was a problem with their requirements or the problem was more difficult than they originally thought.