I'm analyzing a survey, and the requirements of the assignment are to transform the textual responses to a Likert scale. I've used grounded analysis to code the data, but now I'm not sure how to go about converting the coded data into a likert scale. What is the best way to do this?
Those are completely different methods of collecting data. In general, you cannot transform qualitative data into user-reported likert scale-type data. What you can do instead, if you want to report with numbers, is to create a grading scheme yourself, using elements you think are pertinent to whatever grade you give (very much like grading an assignment). Does not have to be "likert". Alternatively, you can follow up with your participants, sending them a short survey.
Guessing you survey was an qualitative open ended question type survey, Reading your question, a usability testing session we did recently came to mind. quantifying the observations was based on things like
how many users were able to complete the task they were asked to perform, at which level (easily, with some difficulty, with assistance)
finding common user pain points, and counting the frequency of the pain points
which features or ui elements they preferred to use to complete the the desk (e.g. buy a green bag, did the user use search or use the navigation bar, did they use filters and/or sort)