What was the doctor's observation?

When Johnsy falls ill with pneumonia and fails to show any sign of recovery, the doctor visits and tells Sue the following:

"She has one chance in—let us say, ten," he said, as he shook down the mercury in his clinical thermometer. "And that chance is for her to want to live. This way people have of lining-u on the side of the undertaker makes the entire pharmacopoeia look silly. Your little lady has made up her mind that she's not going to get well. Has she anything on her mind?"

There is another version of the story in circulation, but the doctor's observation is similar. He questions if Johnsy has anything to live for or if anything is weighing on her mind. He says that Johnsy does have a small chance to live, but she must want to live. He cannot do anything to save her until she is ready to live. Johnsy, however, is determined to die, claiming that she will die when the last leaf falls from the tree outside their window.
Once she notices that the "leaf" is not falling, her will to live returns. The doctor then returns as well, and he makes a new observation:

"Even chances," said the doctor, taking Sue's thin, shaking hand in his. "With good nursing you'll win."

The next day he returns again and notes:

"She's out of danger. You won. Nutrition and care now—that's all."

The doctor's observation in the beginning of the story proves to be true. In order to live, Johnsy needed to want to do so.

When the doctor comes to see Johnsy, who is sick with pneumonia in her Greenwich Village apartment, he tells her roommate Sue that:

"She has one chance in—let us say, ten," he said, as he shook down the mercury in his clinical thermometer. "And that chance is for her to want to live."

The doctor goes on to ask if Johnsy has anything to live for. Sue responds that Johnsy has wanted to paint the Bay of Naples some day. The doctor remains dubious, thinking that is not enough. He says to Sue,

whenever my patient begins to count the carriages in her funeral procession I subtract 50 per cent from the curative power of medicines.

Unfortunately, the case does not look good for Johnsy, who does not have a strong will to live. When Sue finds her counting backwards from ten to nine to six, she asks her what is going on. Johnsy explains that she is watching the leaves fall from the gnarled old ivy vine growing on the house twenty feet away. Johnsy tells Sue that when the last leaf falls from the vine, then she will die. This news is alarming to Sue, who tries to pooh-pooh it as nonsense. However, she remembers the doctor's words that half the battle for Johnsy to live is her state of mind. Therefore, Sue is very worried.

Johnsy is very sick with pneumonia, and her roommate and friend Sue is very worried about her and calls the doctor to come to their apartment in Greenwich Village. The doctor observes in Johnsy that her mental and emotional state are both rather shaky, and he admits that he cannot heal any patient who does not want to get better and who does not want to live. The doctor asks Sue to help Johnsy to recover her enthusiasm for life. Without this energy and will to live, the doctor predicts that Johnsy will succumb to the pneumonia, as he has seen it happen before with other patients. The doctor also wonders if Johnsy's sadness and emptiness could be explained by boy problems, which confuses Sue.