In a jailhouse interview with the Phoenix CBS affiliate, Johnson denied harming their son, saying she told McQueary she had killed Gabriel to get back at him.
"He had ruined my life, and he hurt me, and I wanted to hurt him," she said. "And that was the only thing I could say that would hurt him."
Johnson's grandfather, Bob Johnson, told ABC News that he doesn't believe his granddaughter's story that she simply left her child with an unknown couple.
"I think that she has given the baby to somebody, and I think she knows who it is," he said. "I think it's in San Antonio in somebody else's house, and she just ain't given it up.
"She has an anger-management problem, and she's working on that," he said.
A search of Johnson's car -- found by the FBI nearly two weeks ago in San Antonio -- yielded no obvious clues or evidence of violence, police say.
Motherhood was never really Johnson's strong suit, her grandfather 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."
ABC News' Sarah Netter contributed to this report.