The answer to 'supply line won't flush' is that a clogged or blocked supply line is the most common cause. This can happen due to buildup of debris, mineral deposits, or a partial blockage in the pipe. Symptoms may include slow or no water flow, gurgling sounds, or water backing up in the fixture.
In many cases, you can try to clear the blockage yourself using a plunger, drain snake, or other basic plumbing tools. However, if the issue persists or you're unable to resolve it, it's best to call a professional plumber. They have the specialized equipment and expertise to properly diagnose and fix the problem.