The phrase "sickening degree" refers to something that is so extreme, unpleasant, or unpleasantly extreme that it makes you feel sick or nauseous. Synonyms for this phrase may include "disgusting extent," "nauseating level," "revolting magnitude," "vile degree," "repugnant measure," or "appalling intensity." These synonyms can be used interchangeably with the phrase "sickening degree" to express extreme levels of disgust, repulsion, or aversion towards something. In conclusion, whether you use the phrase "sickening degree" or any of its synonyms, they all effectively convey the idea of something so repugnant that it makes you feel ill.