I don't know what you are taking Xanax for (it's usually prescribed as an anti-anxiety med, but as you are posting in depression, it could be for some other reason). A starting dose is usually 0.25mg not cut in half, but I have to assume your doc knows what he/she is doing. It usually does kick in pretty quickly (although it won't stay in your system for very long).
It should leave you feeling less anxious and give you a sense of calm (albeit a fake one). It could also make you somnolent depending on the dose. If I had to guess, either the dose is not strong enough to do whatever it's prescribed for, or you should be on a different med.
At any rate, you should go back and talk to your doctor. It isn't like an SSRI where the effects take weeks to present themselves, if it were doing something, you would know.
Best of luck,