We have come to a compromise we are pleased with.
Something I had forgotten about earlier (and I think she had too) - is she already has a fixed expense...guinea pigs. She spends about $12 on them a month. So...the cell phone would run her about $25, the guineas run about $12, so that makes 37$ a month of expenses. Out of a 40$ budget. Once I realized this I became even more concerned with her plan. 3$ per month is incredibly little spending money.
Her father and I have asked her to save 37$ for 2 months (which she can put towards her phone) just so she sees what it is like to live on so little money. My suspicion is she will not like it...but her stubbornness may mean she gets the phone anyways. At least she will have 74$ to put towards the $100 phone...which means if she eventually does tire of having no money, she will not be on the hook for many more months while she pays off the phone.
She can also have , for free, a cell phone that no one uses. It is pay as you go. It has texting capability. She has tried it and does not like it as the buttons for texting are tiny and she thinks it is useless - but I think she may be able to adjust to the tiny buttons (and hey - a good portion of her money is at stake). She has agreed to further try it.
We have gone over rules for texting and for the most part she agrees. She does want a phone with a camera, though.