When you seek an extension, be prepared to justify your needing it. There are good excuses for not being able to turn your paper in on time, and bad excuses. Having a lot of other work due at the same time, or a play you have to rehearse for, are pretty bad excuses. We announe the paper deadlines well in advance, and give you two weeks to work on your papers, so that you can anticipate and work around conflicts of that sort. Computer problems are also pretty bad excuses. We're all plagued by them; you need to develop good back-up strategies. Catching malaria would be an example of a good excuse.
If we grant you an extension for your paper, the new due date you are given is firm and must be met.
If your excuse for seeking an extension was a good excuse, there will be no penalty for turning your paper in late. If your excuse was a bad excuse, as it most likely will have been, then your paper will be docked 1/3 of a grade (e.g., from a B to a B-) for every day late, including weekends and holidays.
Don't worry if your excuse for seeking an extension is a bad excuse. We want to talk to you anyway. Every year several students find themselves unable to turn in their assignments on time, and react by panicking and hiding. (They don't come to lecture, they don't return phone calls, etc.) This just compounds their problems. So don't do it. If your paper is going to be late, come and talk to your TA or me.