The parents are on the hook to the hospital, to the myriad physicians involved in the in-hospital care, and for non-covered post-discharge costs. Their financial lives may be crushed absent bankruptcy, which carries its own problems regarding loss of assets and mortgage availability for ex.

The infant is also financially liable but likely uncollectable. The baby's life may or may not be ruined depending on where the US goes w/r/t health insurance coverage for pre existing conditions.