Perhaps one of the most important elements of conflict which has not been suggested by the answer above is the way in which the title suggests a larger conflict. It seems that there is a conflict between the imagination and the ability to see in metaphors and the inability to use the imagination, as expressed in Jig's ability to see the hills that surround them as if they were "white elephants." This of course is linked to the question of the abortion.
Jig's reference to her metaphor results in a squabble between the two lovers, which ends in Jig deliberately choosing to dismantle her vision in an attempt to regain his love and affection. Note what Jig says:
"They don't really look like white elephants. I just mean the colouring of their skin through the trees."
Thus we can see in this comment the way that her abortion is foreshadowed. Just as the imagination is conquered by a dull, practical view of the world, so her body will have the abortion that her lover wants her to have.
I think that there can be several examples of conflict found on both internal and external levels. I think that Jig represents conflict on both levels. The first and most evident is that she is struggling with this issue of the abortion. Jig is an individual who must fight through her own internal doubts about "the procedure" as well as the American's beliefs about it. Through this, Jig is also enduing conflict about whether or not the American truly loves her. This also forms a conflict because it causes her to feel further agony about whether or not she has been foolish in believing his love for her. At the same time, Jig is battling through a larger conflict of what to do. There is little transcendental force present that will relieve her from the pain of choice, and this conflict is another one that she has to endure. The brutal element of ambiguity and doubt are critical elements in Jig's state of being in the world, causing conflict both within herself and her place in the world. In some respects, she is also finding herself conflicted with the issue of time. She wishes to revert time and wonders if her choice in having the abortion will allow her relationship and her life to go back to a previous state. She asks this to the American in wishing to have "things... like they were." In this statement, Jig is embroiled with a conflict over time, seeking to bring the past back in the face of an uncertain future and unforgiving present. For his part, the American's primary conflict is whether or not he can convince Jig to pursue "the procedure." He wishes to live his own life, but endures the conflict that inevitably arises when individual pursuits come into direct conflict with the needs of another.