He was terribly worried that he might have to spend Christmas in the hospital.
Literal
Hospital [at-で] Christmas [object-を] spending must [whether-のではと] he [topic-は] terribly worried.
クリスマスを過ごさなければならないのではと is a complex worry clause — のでは expresses anxious speculation ('what if'), and と marks it as the content of his worry. ひどく心配した means 'worried terribly.'