(CNN) -- While many people get their New Year's countdown clocks ready, Jahi McMath's family is scrambling as a darker deadline looms.
A judge's ruling will allow a hospital to disconnect life support machines at 5 p.m. Monday from the 13-year-old girl, whom doctors declared brain dead after she suffered complications from tonsil surgery earlier this month. Jahi's family, who wants to transfer her somewhere else, told CNN affiliate KGO that they spent Sunday working the phones, trying to line up another option.
The case has drawn national attention and sparked protests from some local leaders who say the hospital that treated her should have provided better care.
Medical ethicists, meanwhile, say the high-profile case fuels a misperception: that "brain death" is somehow not as final as cardiac death, even though, by definition, it is. The case is "giving the impression that dead people can come back to life," Arthur Caplan, director of the Division of Medical Ethics at NYU Langone Medical Center, told CNN last week.
But Jahi's family members maintain that they're hoping for a miracle and want to transfer the girl from Children's Hospital Oakland to another facility. A statement released by family members Saturday and provided to KGO says they are weighing several options.
"Our attorney is in discussions with two facilities that have expressed preliminary approval for accepting Jahi on a ventilator," the statement said. "One is in Southern California, the other is in New York."
Doug Straus, an attorney representing Children's Hospital Oakland, said in a letter to the family's lawyer Sunday that officials are still awaiting specifics from the family.
"To date, there has been no communication from any facility named by you regarding a transfer or requirements for transfer with any of the medical professionals at Children's. The family has not identified any facility with which Children's can have this dialogue. Nor have we been provided with a transportation plan or coroner authorization," he wrote. "As your email and your statements about the facility in the Los Angeles area acknowledge, discussion about performing medical procedures upon a dead body presents unusual and complicated questions. Until there is a definite commitment by a facility to accept Jahi's body upon specified terms, I don't think I can tackle those issues. Please let me know if the family is able to identify a facility."
Jahi was declared brain dead by doctors at the hospital on December 12, three days after tonsil surgery.
Family members and hospital officials fought over her future in court. Last week, a judge ruled she was brain dead and urged both sides to work together to resolves the situation.
But the sparring showed no sign of slowing over the weekend, with family members sharply criticizing the hospital's handling of the matter.
"We wish to acknowledge that Jahi's case, and our stance regarding her right to life, and her mother's right to make decisions regarding her child, has stirred a vibrant, sometimes polarizing, national debate. This was never our intention," the family's statement said. "We have our strong religious convictions and set of beliefs and we believe that, in this country, a parent has the right to make decisions concerning the existence of their child: not a doctor who looks only at lines on a paper, or reads the cold black and white words on a law that says 'brain dead' and definitely not a doctor who runs the facility that caused the brain death in the first place."
The hospital's statement Sunday said they were supporting Jahi's family.
"We continue to do so despite their lawyer's criticizing the very hospital that all along has been working hard to be accommodating to this grieving family," the hospital said.
CNN's Janet DiGiacomo, Elizabeth Landau, Dana Ford, Dan Simon, Michael Martinez and Carma Hassan contributed to this report.