"That was a big turning point for James," she said, "as he was concerned about me getting enough food because he knew that I needed to have enough energy to breast feed both of the children."
By the fifth day, the gas had run out and, along with it, the heat. Sabine had stopped smiling, Kati Kim said, and her cries became "very sad and thin."
By the time nightfall arrived, the whole family was suffering from frostbite and feared the onset of hypothermia -- frostbite's deadly twin -- where basic human existence freezes.
The following day, James Kim, frantic to save his family, had an idea -- to build a fire and send smoke signals skyward.
It took burning all four of their car's tires along with Sabine's stuffed lamb toy -- James Kim called it a "sacrificial lamb" -- to build a fire large enough to send smoke above the tree line.
That small achievement made the couple feel triumphant at first -- but the feeling didn't last.
Terrified for her children, Kati Kim asked her husband to make a desperate pledge.
"I made him promise me that if anything happened to the children and if they died," she said, "that he would take his pocket knife, and he would slit my wrists, and he would lie us all out in the snow together."
By the seventh day, knowing his family could not survive much longer, James Kim chose the only path he believed was left -- he left the car to go in search of help.
What the Kims didn't know was that their story had captured the hearts and fears of the nation. They were completely unaware a massive search already had begun. In addition to search-and-rescue volunteers, James Kim's father, a wealthy owner of an international aerospace company, had commissioned three helicopters from Carson Helicopters Service Inc. and a search team of 25 people.
Meanwhile, two cell phone engineers in Medford, Ore. managed to track the location of the Kims' last cell phone call. But their initial offer to help authorities fell on deaf ears and privacy rule obstacles kept the vital information from rescuers for 24 hours.
"Looking back, I mean, I'm angry," Noah Pugsley, one of the engineers, told "20/20."
"I don't know if I should be surprised or not that, you know, the information was there. All (authorities) had to do was ask us for it, and we basically had to, on our own, go find it out and give it to them on a silver platter," he said.
The engineers' information eventually did help rescuers narrow their search.
By the ninth day, part-time helicopter pilot John Rachor, who had begun his own search for the family, spotted the Kims' car. He radioed for help and within minutes, more helicopters arrived at the site. There they found Kati Kim and her daughters Penelope and Sabine, suffering from frostbite and near starvation, but alive. But Kati was shattered when she learned that James had not yet been found.
"We went from this emotional high to this devastating low of, 'We've only got three; we need four,'" said Joe Rice, operations manager for Carson Helicopters.
Watch the full story on "The Sixth Sense," a special two-hour episode of "20/20" at 9 p.m. ET.