Can part-time workers qualify?
It is likely that you do qualify as a part-time employee. The most important qualifier is income. Generally, you must make less than 50% of the Area Median Income (AMI) of that area to qualify. Keep in mind that there are other significant qualifiers such as housing and criminal history.
Also, when calculation income, your qualification depends on the entire household's income, just not your own. For example, if you only work part-time, but have a significant other that works full-time, both of your incomes must fall under the income limit for a two-person household.