Test Driven Design for postgres procedures
Test-Driven-Development (TDD) is an ideology. You can usually poke holes in implementations; and generally you sacrifice convenience and efficiency in any implementation of TDD -- which is why you have to sell it, and why it's not intuitive. You're running up against a problem which is one of the terminus ad quem of testing. You're likely trying to be a purist and often people get lost in the woods in that pursuit.

When you create a website, generally you don't test whether or not the framework, is producing a valid HTTP response. Such a test resides in a different layer, and you should only use frameworks and libraries that have a rigorous test suite that test their own domain. Anything you do to test a valid HTTP response should come up in end-to-end testing (with something like Protractor).

Think of PostgreSQL as a "framework" at a lower level that manages your data. You need to test how you get things in and get things out. Most of what PgTAP does is absolutely overkill. A ton of it is validating the schema -- how would that even work with TDD? Take..

CREATE TABLE foo ( a int PRIMARY KEY, b text, c uuid );


You're going to test 


foo exits and is a table
a is an interger
b is a text field
c is a uuid


All of that is well tested to be the result of,

CREATE TABLE foo ( a int PRIMARY KEY, b text, c uuid );


You're going to drive yourself nuts testing that. If you need to validate two schemas are the same, you can simply pg_dump --schema and diff the two. You can actually generate, with great ease, a full schema test suite that tests everything.

As far as what you need to test: any procedural code in the database. Generally we do this with test-data as PostgreSQL does, or by simply having a test-database which your framework can connect to and test the procedural code like everything else.

Shy of that, you want Fat Model, Skinny Controller (put as much as your data-manipulation logic in the model) so you can use it outside of your web app, and testing that should be done like anything else in whatever language you prefer.