I'm equally worried, more so for the TOEFL than the GRE. For some weird reason, TOEFL scores take at least seven working days to be 'shipped' (what, they send paper reports???!), and another seven working days to reach the recipient. Combine this with the fact that many universities match scores manually, and it takes three weeks for your scores to show up at some places. GRE scores are better, usually reflecting within a day or two of the order. Though I faced your problem with one university, which updated both a week after the deadline, even though I'm sure the scores arrived well in advance since other recipients updated them immediately. It wasn't a hard deadline and I can only hope it doesn't cause problems to my application, but it's frustrating given the time and money you spend on each application. I can't order all score reports in one go either due to financial reasons, and I can't for the life of me fathom why the whole process is so slow given the kind of money they make you pay simply for xeroxing the same report and mailing it to a university.
Now the same tensions for two programs with explicitly hard deadlines in mid-January, and I can only hope the GRE and TOEFL reports I ordered today (had to borrow money from parents) reach them in two weeks and that they'll be updated promptly.
I may be amazingly wrong, but I find both exams utterly pointless, a huge drain on finances (average masters student in a developing country), and there is something very racket-y about paying for 'additional reports'.
Ha, rant over.