Hi guys. All I can do is tell you about my experience applying last year. Of course, bear in mind that I was applying for Dramatic Writing and so if you're applying for another program, things might be a little different.
I certainly didn't get all of my materials in last year by December 1st. In fact, I didn't even finish the online application. I had written the school off because I figured I had missed the deadline.
However, a couple of weeks after the deadline, NYU sent out a mass email telling all those who had at least started the online application that they would grant them a slight extension and gave them contact information for who to talk to if they wanted to take advantage of this extension.
I did, and was told just to make sure that I finished the online application as soon as possible, that was the important thing, and the next important thing was to get in my creative materials. I was told that letters of recommendation and transcripts often come in late.
I finished the online application, and they told me just to fax them a copy of my transcripts (even though online they say that they need official). Usually, they really only end up needing official if you're admitted, and then they'll contact you seeking those. I contacted my recommenders pronto, and they got their recommendations in online as soon as they could, but there were still delays (trouble submitting online, emails not received, etc, etc.).
Then, I thought I had gotten everything in, and it was about the end of January before I was informed that they hadn't yet even received my creative materials (full length play), but that they would be granting me an extension to get it in.
By the end of the whole ordeal, it was toward the end of January before they received all of my materials, and I ended up getting waitlisted for the program.
I applied again this year, and I've gotten all of my materials in on time except for one recommendation. I simply emailed Tisch grad admissions about an extension, and quickly heard back from Peter Gerena (great guy, an ENORMOUS help) that it would be no problem and that they would accept the recommendation late and that it would not detrimentally affect my application.
Also, I can tell you that, after working in a Graduate Program Admissions office for over a year at Harvard that many admissions offices (I don't know about all of them, of course) will give a deadline well in advance of when they actually need all of the materials, because they know that there will be delays in applicants getting their materials in. It's a psych-out move.
I would suggest just taking a deep breath, sending the admissions office a very pleasant email and waiting to hear back while trying not to panic too much (I know from experience that it can be difficult).