I've done Extreme Programming (cf. _Extreme Programming Explained_ et al) approaches on a team of about that size and it worked okay, but the deadlines weren't as hard. The pair-programming aspects helped keep everyone informed about what sort of implementation decisions and tools were being made (quite useful on a team of eight) without bogging things down with meetings, and it also helped keep people very focused... and also honest about actually being TDD, as in "don't write a single line of code which isn't necessary to make some test pass", which helps keep you from overengineering some part of the code and helps you meet deadlines.

But it's hard to say whether it'd work, because (a) your problem is described very vaguely, and (b) your team might not be up for it (the classic problem), and (c) even if they were up for it, it's a process they likely haven't practiced much, so that makes it harder