Please allow me to start my response with a preface about the nature of literal interpretation.
Traditionally, through the Church's history, literal interpretation has not meant "reading the text to mean just what it seems to me to mean." At least as far back as St. Augustine we see that this is so. Rather, the literal sense of scripture was contrasted with the spiritual sense. The literal sense is the meaning intended by the human authors at the time of writing, and the spiritual senses are the meanings embedded into the text by the Holy Spirit at that time and thereafter. In his The Literal Meaning of Genesis, he asserts theological reasons to believe that the world was created, together with all its component parts, simultaneously. He also make the case that the literal meaning of the Genesis creation accounts are figurative. See Wikipedia's summary of Augustine or an excerpt from The Literal Meaning of Genesis to see how early and how prominent a teacher of the Christian faith held this view.
How can the literal meaning be figurative, though? And moreover, when did people start thinking that a "literal meaning" was a "face value" reading, or "the text as it appears to me"? As to the first question, if we bear in mind that many writers often write figuratively to convey a meaning or moral, and that they do not always start by telling us that this is their endeavor, but rather, expect us to understand that fact, we can see how the same thing happened in antiquity. Nobody in modern times expects the story of the Three Little Pigs to be either (a) false or (b) literally about three talking pigs and the talking wolf who stalked them. Rather, we all know that it is about a moral, about doing things right the first time as a security against future adversity. Nobody needs to tell us that. Small children pick up on it because they know that pigs do not talk and that their parents, telling the story, are not fools who think that pigs talk.
As to the second question, I do not know that I can put an exact date when the shift in understanding about literal interpretation happened. It certainly happened after the medieval period because none of the medieval theologians interpreted Genesis as modern scholars might. In fact, if anything their vice was the contrary vice - they are accused by the Reformers of over-symbolizing every account and story. I suspect Luther's insistence on the ready interpretability of Scripture may have facilitated this shift. Certainly by the time of the fundamentalist revival of the early 20th century, the practice was well established in the Protestant world, and even earlier, since the Protestant liberal theologians of the mid-19th century reacted against the practice of interpreting scripture at face value, of asserting that the "plain meaning" of Scripture is what the scriptures plainly meant.
I make this preface, although it is actually the bulk of my response, because it's a game changer. If the words of Genesis 1-3, say, aren't meant to be taken at face value, then all the questions we ask of them shift. It suddenly doesn't matter so much if a day is a 24-hour period or a period from sunset to next sunset. That is a good thing, because obviously, if the words of the account are to mean what they plainly seem to mean to modern readers insisting that the story be taken at face value (as we never take our own stories), then the text becomes hopelessly confused - which is a far worse thing than for the reader to be hopelessly confused. After all, how could there be sunset-to-sunset periods before there is a sun? That question does not answer itself plainly. And moreover, the concept of a 24-hour period only makes sense in the context of a sun shining on a more-or-less equatorial environment, where days are about the same length all year, and nights about the same length as the days.
But if we can set aside how long a "day" is supposed to be and whether it is supposed to represent any particular period of time at all, as Augustine did, we can get down to the important work of finding the actual intention of the author (the literal sense, according to Augustine). If that literal sense, rather than our "literal reading", has embedded in it a moral value, a spiritual teaching, or a truth about the nature of God or the Kingdom, we may miss it altogether by arguing about geological questions the text was not intended to discuss and that frankly did not interest our forefathers in faith.