The family of Archie Battersbee are making an urgent application to the European Court of Human Rights to stop his life support from being removed.
They were given until 9am this morning to submit the application after the Supreme Court yesterday refused an appeal.
Barts Health NHS Trust has told the family that Archie's life support will be withdrawn at 11am if the application is not submitted in time.
The family and their lawyers have expressed frustration at the tight deadline and the Trust's refusal to allow Archie to be moved to a hospice.
"This is cruel and we are absolutely appalled," said Archie's mother, Hollie Dance.
Following an application by the family, the United Nations Committee on the Rights of Persons with Disabilities (UN CRPD) asked for a temporary stay on the withdrawal of Archie's life support while it considers his case.
The government said in its submissions to the Supreme Court that interventions by the UN CRPD are "not binding" under international law.
Archie, 12, was found unconscious in his home in Southend, Essex, with a ligature around his neck. His mother thinks he may have been taking part in an online challenge.
He has never regained consciousness but Ms Dance maintains that she has seen improvements in her son and that he should be given more time to recover.
His family are being supported by the Christian Legal Centre, who are asking for prayers.
