Seventeen-month-old Emilio Gonzales suffers from a terminal neurological disease and cannot breathe on his own.
His doctors consider further treatment to be futile and potentially painful. Last week they gave his family 10 days to find another hospital for the boy.
But a nationwide search for a new facility has failed, and his mother Catarina wants a judge to intervene.
If the court refuses to prevent the hospital ending Emilio's treatment, his support is likely to be switched off on Wednesday.
'Aggressive, invasive'
Catarina Gonzales, 23, denies that her son is unable to respond as doctors say. She says he smiles and turns towards voices.
"It's not like he'll just drift off quietly"
"I know my son is going to die," she said. "I just want him to go as natural as he can. Not by someone telling me that we're going to take him off the ventilator because there's no use."
Family lawyers also argue the boy's death would essentially be by asphyxiation.
This would be a painful way to die, they contend, as the law would prevent hospital workers from giving the boy drugs that even death row victims are entitled to in order to ease the pain of execution.
"It's not like he'll just drift off quietly," says lawyer Joshua Carden.
"The care is very aggressive and invasive"
"The care is very aggressive and invasive," says lawyer Michael Regier, adding that for some staff at the hospital keeping the baby alive by means which may hurt him "is ethically and morally repugnant to them".
Emilio is thought to have Leigh's Disease, a degenerative condition which causes brain tissue to die.
'Not enough time'
The boy is at the centre of a dispute brought about by a law signed by George W Bush when he was governor of the state of Texas. The legislation allows a hospital, rather than families, to make decisions in "medically futile" cases.
The 1999 law has been attacked by patients' rights organisations, disability groups and Texas Right to Life, primarily an anti-abortion lobbying body.
One of their principle arguments is that the 10-day deadline hospitals are allowed to impose does not offer families enough time to find another suitable facility for the patient.
Texas Right to Life, which is helping the Gonzales family, says it has been involved in more than 24 such cases in the last 18 months.
But supporters of the law say the cases are rare, and that in the vast majority of cases family and hospital reach agreement on the patient's treatment.
^ Back to top | BBC Sport Home | BBC Homepage | Contact us | Help | ©
~RS~q~RS~~RS~z~RS~52~RS~)