It's certainly possible to do xUnit style SQL unit testing and TDD for database development - I've been doing it that way for the last 4 years. There are a number of popular T-SQL based test frameworks, such as tsqlunit. Red Gate also have a product in this area that I've briefly looked at.
Then of course you have the option to write your tests in another language, such as C#, and use NUnit to invoke them, but that's entering the realm of integration rather than unit tests and are better for validating the interaction between your back-end and your SQL public interface.
http://sourceforge.net/apps/trac/tsqlunit/
http://tsqlt.org/
Perhaps I can be so bold as to point you towards the manual for my own free (100% T-SQL) SQL Server unit testing framework - SS-Unit - as that provides some idea of how you can write unit tests, even if you don't intend on using it:-
http://www.chrisoldwood.com/sql.htm
http://www.chrisoldwood.com/sql/ss-unit/manual/SS-Unit.html
I also gave a presentation to the ACCU a few years ago on how to unit test T-SQL code, and the slides for that are also available with some examples of how you can write unit tests either before or after.
http://www.chrisoldwood.com/articles.htm
Here is a blog post based around my database TDD talk at the ACCU conference a couple of years ago that collates a few relevant posts (all mine, sadly) around this way of developing a database API.
http://chrisoldwood.blogspot.co.uk/2012/05/my-accu-conference-session-database.html
(That seems like a fairly gratuitous amount of navel gazing. It's not meant to be, it's just that I have a number of links to bits and pieces that I think are relevant. I'll happily delete the answer if it violates the SO rules)