Certainly, Jig's pregnancy is the catalyst for the character development in the short story. It becomes evident that the American and Jig consummated their relationship and as a result she is pregnant. Hemingway makes it clear that the father is the American and that there could be no sense of mistaken impregnation. The fact that Jig is looking for affirmation from the American regardless of the decision about "the operation" reflects this. Additionally, the repetition of the refrain of "it's an awfully simple operation" conveys that the American impregnated her and seeks to eliminate the condition and attachments that pregnancy brings with it. In a larger sense, I think that part of Jig's own character is wrestling with the reality of how she could allow herself to be pregnant and how such a decision has cast a rather looming shadow on her relationship with the American. Regardless of what happens, some bar or point has been crossed and she recognizes that. It is here where the questioning of her own pregnancy and the implications that result from it become a significant part of her character's analysis and development.
In the modern era it is fairly easy for a woman to avoid getting pregnant if she wants to. But this story is about the 1920s. There was no such thing as a birth-control pill or a morning-after pill or antibiotics. Contraceptive measures were primitive and unreliable. Young people today often fail to realize how much things have changed in the past hundred years or so. Looking around my small apartment, I can see many things that were nonexistent and even undreamt of in the 1920s. There were no microwave ovens. No refrigerators or freezers. No garbage disposals. No electric clocks. No synthetic fabrics. No plastic items. Certainly no computers or even electric typewriters. No ballpoint pens. No television. Radio was very crude and limited in range. No recording devices for home use, e.g., no telephone answering machines. Virtually no air transportation. No wristwatches. Obviously no cell phones. No electronic gadgets.
Jig and the American have been together for a long time. It should have come as no surprise that she became pregnant. They are young. Sometimes people get careless, don't they? Nature has a way of playing tricks on lovers. The name of the game is procreation. Jig may have gotten pregnant deliberately, hoping that the man would accept it as a fait accompli and agree to give up their nomadic existence, settle down, become a father and a breadwinner. (This would certainly not be the first time such a thing had occurred.) He is pressuring her to get an abortion, but she is subtly pressuring him to let her have the baby. She is making him feel like a heel--which he is. He needs that second anis del toro.