The family had switched from burning wood to an electric heater and it was the only heat source in the living room where the family slept, James Tucker said.
Blair said Tucker lived in the home with the children's father, Billy Wilfong. The two weren't married but had been together for about seven years, she said.
Blair identified the children as 5-year-old Dakota Lee; 4-year-old Tyler Lane; 2-year-old Cheyenne and Emily, who was 6 months old. She said she watched the kids often and that they loved to play outside and watch TV together.
"They were good kids, you couldn't ask for no better," Blair said.
Dakota liked robots and cartoons; Tyler was a monster truck fan and Cheyenne enjoyed playing with Barbie dolls.
They were close-knit playmates, relatives said.
"That might be why the Lord took all four of them at the same time," Elkins said.
Roberts said the bodies would be taken to the medical examiner's office in Frankfort, and it could take several days for positive identifications. The infant was found within a foot of the father, and all the victims were within about two feet of each other.
"They could've been overcome by that smoke and just went into like a deep sleep," Roberts said. "They just couldn't make it out."
Fire investigators said the blaze was accidental and broke out in the living room where the space heater was found. A cause had not been determined.
No officials could recall a similar deadly blaze in Kentucky since 10 people, including six children, were killed in a house fire in Bardstown in February 2007.
County Judge-Executive spokesman Brandon Roberts said there's been no similar fatal fire in Pike County in recent years.
"I can't remember a whole family perishing in a fire in my lifetime," Roberts said. "It's just, 'Oh God.'"
Associated Press writers Dylan Lovan and Brett Barrouquere contributed to this report from Louisville.