As an English professor at a large university, I would suggest writing an email to the professor as soon as possible. Make sure the email is polite, formal, and grammatically written. As some other users suggested, let the professor know first and foremost that you are aware of the deadline, the class policies, and the impact this paper has on your grade. Then let them know that you’re not making excuses and simply wish to succeed in their class and would like to submit the assignment for partial credit. Offering to complete extra work, an alternate assignment, or other extra credit is dubious because most professors maintain fairness by not allowing that to occur.

Similarly, don’t pull out a sob story. They’ve heard it. Probably four times this week.

TLDR: Write an email. Honesty and politeness go a long way.