I'm going to play devil's advocate here. It's stated that taking points off the grade for a late assignment "replicates the deadline criterion of the work world". No, it doesn't. In my field, if you are late, you lose the client, you lose money and, ultimately, you will lose your job. Do this enough, you lose your business. There are no valid "Oh, we didn't get finished on time...." excuses because client deadlines are written in stone.
Added Note: I give each student a sheet outlining the project and the due date and time. I also put this info online where all students have access 'in case they lose their info sheets'. Students know I do this, and many have had me for multiple terms, yet still try to say they didn't know the deadline.
Now, again as devil's advocate (I'm reiterating this point), please defend how a missed deadline and merely taking a percentage off for each day it isn't turned in replicates the real world? I am a strong advocate at the college/higher ed level that if a deadline is missed, the student gets a '0' right off the bat. Please explain why I should back down on this belief.