In Arizona, the most they can take from your wages is 25% each pay check. You should request a hearing and ask the judge to lower it. Most judges will lower it to 15% if you file an answer and let the judge know it will create a hardship.
The answer to your question is that financial hardship is not relevant to the question of whether wages can be garnished, but it is relevant as to the amount that can be garnsihed. The above attorney described the limit of garnishment due to hardship.