What tool would likely be used in a household setting for unclogging toilets?

The use of a plumber's snake is highly effective in a household setting for unclogging toilets. This tool is designed specifically for navigating through the bends and curves of plumbing pipes. Its flexible design allows the snake to reach clogs that may be deep within the drainage system, effectively breaking up and removing obstructions without damaging the pipes.

A plumbing auger, while similar, is typically used for larger drain lines or more significant plumbing issues, making it less practical for common household toilet clogs. A sump pump is used to remove water from basements or flooded areas and is not meant for clearing clogs. The fixture unit, on the other hand, is a term related to plumbing design calculations rather than a physical tool used for unclogging. Thus, the plumber's snake stands out as the most suitable and commonly used tool for this specific household task.