It isn't revealed until the end of the story that Phoenix is on a mission to get medicine for her grandson. When Phoenix does finally arrive at the doctor's office, it is the Nurse who informs the reader about the motivation for the journey: Phoenix's grandson. After a passing forgetful spell, Phoenix remembers that she has come to get medicine for her grandson. In describing her grandson, this is the only time she is ingratiating. At all other times, she is calm, determined, and confident. This indicates her determination.
She is confident when she needs to be and humble when she needs to be. In the case of the latter, she is determined to get medicine for her grandson and won't let any potential frustration on her part or condescension from others get in the way of that determination. When the nurse comments that the grandon's throat has never healed, Phoenix responds that it has not healed but he is still alive. She also indicates that her love for her grandson has become her reason for being, her reason for continuing to embark on a journey that is probably too dangerous for someone her age:
We is the only two left in the world. He suffer and it don't seem to put him back at all. He got a sweet look. He going to last. He wear a little patch quilt and peep out holding his mouth open like a little bird. I remembers so plain now. I not going to forget him again, no, the whole enduring time. I could tell him from all the others in creation.
Phoenix, after receiving another "charity" nickel from the Nurse decides to use the money to buy her grandson a windmill. Clearly, Phoenix, in the spirit of her name, rises to the challenge again and again to care and make the journey for her grandson. Welty wrote that it is not the circumstances but the "habit of love" (the habit of loving her grandson) that drives Phoenix to overcome all obstacles.