The author William James talks about the importance of a "momentous option" in his lecture "The Will to Believe" published in 1896 in which he generally explains the importance of believing in certain concepts that have not been scientifically proven. One of the beliefs explained in the lecture, is the momentous option which refers to the specific moments in life that are presented normally for a really short period of time in a spontaneous way that lead to decisions almost forced, but that represent significant events in life.
"The Will to Believe" is a lecture by William James. It was first published in 1896 and defends the adoption of a belief without evidence of its truth.
In this lecture, James defines a "momentous option" is an irrevocable option for significant stakes. A momentous choice is supposed to be taken at the moment, because there will not be a second opportunity to make it.
Therefore, a momentous option is a choice between alternative beliefs that cannot be postponed (there won't be a second opportunity) or, at least, can only be postponed with significant loss.