Sonia del Cid Iscoa has been in a coma in St. Joseph's Hospital and Medical Center since she gave birth to a daughter prematurely April 20, The Arizona Republic reported Sunday.
The newspaper reported that Iscoa is in the United States legally through temporary-protection status.
The hospital, part of Catholic Healthcare West, can treat patients for acute emergency needs but because the facilities aren't built to provide long-term care, patients must be transferred when the medical crisis has passed.
John Curtin, Iscoa's attorney, said the hospital is attempting to deport Iscoa.
"You don't take someone who's unconscious and helpless and move them out of the country over the objections of their family," Curtin said. "I understand the hospital's concerns about being paid. But the hospital cannot do what the U.S. government would not be allowed to do."
A Maricopa County judge Friday gave Iscoa's family until noon Tuesday to put up a bond of $20,000 to ensure Iscoa's care while the case is heard.