I've tried everything I can think of. I did the appeal process through the department, and didn't get anywhere. Though the project is in engineering, my POI made it clear that they don't have any funding that they could use to support me and I have had very limited success with outside sources.
The department's final offer was a TA position for $19,800 per year, but I have $600 per month in loan payments for $7,200 per year. I applied for and won a $1,500 per year scholarship from the university's alumni association, but that still means trying to live on $14,100 per year in an area with fairly high living costs. I've come to realize that unless they can make an exceptionally generous offer, it just not going to work, so I'm just looking for some help declining the offer as respectfully as possible.