Following up on what the esteemed Anonymous Monk wrote, I would suggest looking at Test::MockModule. I often run into the same situation and find that if I structure my code right I can mock calls to LWP, etc. and return known values so I can see how my code handles auth failures and various return codes.

Basically, you want to mock any method call that is outside your module that depends on a given resource already existing. Tedious, sometimes, but it can give you confidence that your code will handle what is thrown at you. I presume that you are really interested in your code dealing with various return values so being able to supply known good and bad results is what you want for testing.

I recall seeing a couple of modules designed specifically for mocking HTTP calls, try doing a CPAN search for Test::Mock and see what turns up.