The girl's doctors at the University of California, San Francisco, Medical Center have balked at the request and referred it to the hospital's ethics committee.
California state prison officials also need to sign off on the proposal and they are questioning the cost to the taxpayers of maintaining the prisoner on dialysis. The bill has been estimated at $40,000 a year.
At the center of the controversy is Renada Daniel-Patterson, who was born with one kidney, an unhealthy one. She has undergone two previous transplants. The first kidney, transplanted when she was 5 years old, was rejected.
The second kidney came from a father she hardly knew who was doing time at California State Prison on burglary and drug charges.
"He called out of the blue," Renada's mother Vicki Daniel, recalled. Since the transplant, Renada and her father have kept in close contact, exchanging letters and phone calls.
For two years, Renada lived as a healthy teen, but she often skipped her medication because she didn't like its side effects. As a result, the kidney has begun to fail.
Now her father, who still has three years left to his prison term, is offering to give her his one remaining kidney, sentencing himself to a life on dialysis.
"I think it's great and [it shows] he loves me,"Renada told CBS This MorningCo-Anchor Thalia Assuras. "If that's what he wants to do, that's what he wants to do. And I appreciate it."
Her nephrologist has refused to perform the surgery, citing the Hippocratic oath to "first, do no harm." When the family appealed, their request was referred to the bioethics committee, which is still considering the matter.
Doctors say her father, Folsom prison inmate David Patterson, could survive for a time without kidneys, which filter toxins from the blood, but his life would be shortened and his health constantly threatened by infection.
"I'm worried what might happen to him," Renada said, "but the same thing that will happen to him will happen to me [if I don't get the transplant]."
Patterson also would require costly dialysis treatments, which concerns prison officials, since the corrections system would have to pick up the costs of the treatment and of transporting Patterson several times a week to a medical center where dialysis is performed.
"I think this is a family issue," Vicki Daniel said. "We have decided this for our child, and we want to move forward with it."
Skeptics have questioned whether Patterson is hoping to shorten his prison sentence with his sacrifice. Vicki Daniel scoffs at that: "He wants his daughter to be able to do the things he never did. And she will, if she's given the opportunity."
The Rev. Dr. Lorenzo Carlisle, pastor of Oakland Comunity United Church of Christ and a family friend, calls Patterson a hero. "There is no greater love than to lay down your life for a friend," he said. "Mr. Patterson is a hero, a father, and a friend. He is willing to lay down his life. And I think we should look at that."
James Childress, professor of religious studies and medical ethics at the University of Virginia, agreed Patterson's willingness to sacrifice his kidney for his child is worthy of praise.
"But matters are not simple in the area of organ donation because here the effort to rescue a family member through a donation presupposes the cooperation and expertise of medical professionals," he said.
The family may not be able to find a surgeon willing to perform the operation even if the procedure is approved by the ethics committee.
"We don't know for sure whether he could function well," said Childress. "Ten percent of the people who go on dialysis do not function well."
Everyone agrees that it is a last resort. If a donor kidney can be found quickly, Patterson won't need to give up his. However, Renada's condition has deteriorated in recent months and her mother said she shouldn't be required to wait.
"We put out a call all over the nation to have people call in, and we want them to continue to call, to try to see if they will match her,"she said. "But he will be our last resort and we believe this will happen."
Meanwhile, Renada and her family wait. Renada says she was in touch with with her father this weekend. "He told me he loves me, hopes I feel better, and he's waiting to see what the doctors are going to say."