Dan North has suggested that there is no such thing as test-driven design because the design is not really driven out by testing -- that these unit tests only become tests once functionality is implemented, but during the design phase you are really designing by example.
This makes sense -- your tests are setting up a range of sample data and conditions with which the system under test is going to operate, and you drive out design based on these example scenarios.
Some of the other answers suggest that this is based on YAGNI. This is partly true.
Beyond that, though, there is the issue of complexity. As is often stated, programming is about managing complexity -- breaking things down into comprehensible units.
If you write 10 tests to cover cases where param1 is null, param2 is null, string1 is empty, int1 is negative, and the current day of the week is a weekend, and then go to implement that, you are having to juggle a lot of complexity at once. This opens up space to introduce bugs, and it becomes very difficult to sort out why tests are failing.
On the other hand, if you write the first test to cover an empty string1, you barely have to think about the implementation. Once the test is passing, you move on to a case where the current day is a weekend. You look at the existing code and it becomes obvious where the logic should go. You run tests and if the first test is now failing, you know that you broke it while implementing the day-of-the-week thing. I'd even recommend that you commit source between tests so that if you break something you can always revert to a passing state and try again.
Doing just a little at a time and then verifying that it works dramatically reduces the space for the introduction of defects, and when your tests fail after implementation you have changed so little code that it is very easy to identify the defect and correct it, because you know that the existing code was already working properly.