The couple worried about tiny Sabine and Penelope, who was tired, cold and wanted a hot meal. By the third day, Kati Kim decided to breastfeed both her children.
"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. offered to help locate the Kims by tracing their cell phones and, despite several obstacles, eventually managed to 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 a special two-hour episode of "20/20" tonight at an earlier time, 9 p.m. ET for more on Kim's story.