No this is a deadline they set themselves - the whole "ethos" of timeteam is to show that archeology can be fun and doesn't require a three year research grant
I think that it's because it's done over a weekend. As I understand it, they all have jobs at universities, and have to film when they are free. As Time Team is still controversial in archaelogical circles they probably wouldn't be allowed to take loads of time off to do it.
if by "jobs at universities" you mean they are lecturers then correct but they're not there 5 days a week lecturing. I'm pretty sure the deadline is to prove that archeology can be done speedily
I'd also say that it's to add a sense of urgency - it's so much more exciting when you know they only have 3 days to prove something or other. Wouldn't it be boring if it said, "And in March Phil discovered... but by Novermber Stuart had totally disagreed with him..." etc. Mind you, I wonder how quickly they get things done in their "real" jobs...