The phrase "keeping one shoulder to the wheel" means to continue working hard and persistently towards a goal or task, even in the face of obstacles or challenges. There are several synonyms for this phrase, including "staying the course," "persevering," "sticking to one's guns," "committing to the task," and "pursuing diligently." These synonyms all suggest a strong dedication to the task at hand and a willingness to work hard and overcome setbacks in order to achieve a desired result. Whether in the workplace, the classroom, or in personal pursuits, these synonyms remind us of the importance of perseverance and focus in reaching our goals.