A search of Johnson's car -- found by the FBI last Tuesday in San Antonio -- yielded no obvious clues or evidence of violence, police say.
Motherhood was never really Johnson's strong suit, Bob Johnson said.
"She discovered after eight months that there's more to this parenting than she wanted to get involved in," he said. "It was not her thing. She was into fashion."
Police have searched the Smiths' home but found no clues to indicate where Gabriel might be.
Carbajal told "Good Morning America" that Tammi and Jack Smith have no legal right to the child.
"We want to be clear that the court has made a determination here in Arizona that Logan is the father," he said. "Logan has stated numerous times that his desire is to raise his son Gabriel."
McQueary has charged that the Smiths pressured him into giving up the rights to his child.
"When Gabriel disappeared, they said, basically, 'You know, if you care about your son and you want him back, you will sign the paperwork and she will bring him back to us and you will know that he is safe,'" McQueary said.
The Smiths denied that accusation and said they were simply passing on that message from Johnson and that they told McQueary they knew such papers wouldn't hold up because he signed them under duress, though it might bring the baby back.
"The father and Jack and I were in constant contact when we found out Elizabeth fled with the baby," Tammi Smith said. "When we finally got to speak to Elizabeth, she was so angry with the whole situation and told me, 'I have one message to give to Logan.'"
That message, Smith said, was sign the papers and the baby will be brought back.
Anyone with information about Gabriel Johnson is asked to call the Tempe Police Department at 480-350-8311.