No, the debt is his before you were married so your personal savings can't be attached for his child support arrears. He must pay child support or he can be jailed if the ex persues this through child support enforcement agencies, so the best course is for him to contact the court ordering support and petition for modification if it is set at a rate he is unable to pay; ordinarily if the non-custodial parent can show a change in earnings the court will adjust the amount.
