The answer to 'emergency plumbing won't flush' is that a clogged or blocked toilet is the most common cause. This can be due to a buildup of debris, foreign objects, or even a problem with the toilet's internal mechanisms. Symptoms may include the toilet filling up with water but not flushing properly, slow draining, or water backing up.
In many cases, you can try to address a clogged toilet yourself using a plunger or a drain snake. However, if the clog is severe or you're unable to clear it, it's best to call a professional plumber. They have the tools and expertise to safely and effectively unclog the toilet and diagnose any underlying issues.