Sergio Rojas and Linda Martinez were told two weeks ago they have until March 4 to leave the country after their application for permanent residency was rejected.
But they have the option of leaving behind their youngest son, who has a rare medical condition, as a ward of the state. The three-year-old, who was born in the Yukon, suffers from skull deformation and a neck muscle disorder.
The family understands the option technically, but hasn't come to terms with it emotionally.
"We can't go without him," Martinez said Monday at Whitehorse International Airport.
"It's scary. In Mexico, there's not anything for Jonathan. ... I feel very bad."
Martinez sobbed as she bid farewell to her partner and their other son, 7, who were taking an early flight to Vancouver to handle pre-departure paperwork. She and Jonathan are slated to join them on Wednesday.
Jan Stick, NDP health and social services critic, called the family's situation "a human tragedy."
"To me, this is just such a cruel decision that no family should have to face," she said at the airport.
Stick said the ideal outcome would permit the family to remain together in Whitehorse as landed immigrants "and be able to work and be a part of this great community."
The family had applied for permanent residence on compassionate grounds, but their application and a subsequent appeal was rejected.
Citizenship and Immigration Canada's website states immigrants should apply for residence on humanitarian and compassionate grounds if they "would suffer excessive hardship" by returning to their home country.
The federal department said it could not speak to the case without the family's written consent.
Yukon MP Ryan Leef spoke with Rojas over the weekend and met with Immigration Minister Chris Alexander on Monday in Ottawa.
Jonathan suffers from plagiocephaly — sometimes referred to as "flat head syndrome" — and congenital torticollis, which must be treated with specialized therapy.
He spends much of each week at the Yukon Child Development Centre and has received treatment at the B.C. Children's Hospital.
The centre wrote a letter stating Jonathan would have difficulty accessing therapeutic services in either Mexico or Nicaragua, his mother's country of origin.