Brian Peterson is charged with murder along with 18-year-old Amy Grossberg, mother of the baby, who was put in a plastic bag and dumped in a rubbish bin outside a hotel last week.
Joseph Hurley said Peterson's family had considered sending the 18-year- old abroad to avoid prosecution, but he had talked them out of it.
The lawyer described Peterson, a student at Gettysburg College in Pennsylvania, as "a combination of dazed and extremely fearful" since prosecutors said they would charge him and seek the death penalty. He said Mr Peterson would surrender today and plead innocent to a first-degree murder charge, so that the family would not be charged with harbouring a fugitive. Mr Hurley said on ABC's Good Morning America that the mother had considered fleeing with her son.
When a mother hears her son is facing the death penalty, he said, "one of the immediate thoughts is, `I'm getting them out of here'. "
Ms Grossberg, of New Jersey, was arrested Monday and was being held without bail. Both she and Mr Peterson could be sentenced to death if convicted.
Mr Peterson and Ms Grossberg "never went into that motel with the idea, `We are going to kill a child'," Mr Hurley said.
On 12 November, the police authorities say, Mr Peterson had driven three hours from Pennsylvania to Newark to pick up Ms Grossberg at the University of Delaware. They checked into a motel, where Mr Peterson helped deliver the baby boy and put him in the rubbish bin.
Police believe Mr Peterson is the baby's father but want to compare his blood with the baby's to for confirmation.