We should also consider different cultural approaches to time. Cultures differ in striking ways in their attitudes toward time. Among these differences are differences concerning punctuality and "keeping to the clock." First, people can focus on the "objective" passing of time as shown by a clock. We may call this clock orientation. Second, they can focus on the more subjective, interactive time that they experience in the rhythms of human events. Human beings interact with one another in social groups or interact with created things, such as when they celebrate a wedding or harvest a field. .. We may call this focus interactive orientation. ... [Vern S. Poythress, Redeeming Science: A God-centered Approach (Wheaton, IL: Crossway, 2006), 138]
How does all this apply to Genesis 1? If one goes to Genesis 1 with a clock orientation, one focuses primarily on how long it took, as measured by a clock. But if one goes to Genesis 1 with an interactive orientation, one asks what important events took place, and what was their human social meaning. ... (Ibid., 139)
The argument made by Poythress, in his promotion of the analogical day position, is that the very notion of 24-hour days of creation is a very modern and Western phenomenon. Ancient societies like ancient Israel do not have a "clock orientation" but an "interactive orientation" and therefore the fixation on the length of days is unbiblical.
It is granted that modern Western societies have a "clock orientation." Yet, this objection to the 6-24 view is rather strange. If the objection merely wants to claim that it may not exactly 24 hours, then of course YECs are not tied to exactly 24 hours 00 minutes 00.000 seconds! The "24" in the 24 hours of the day is not meant to insist on a particular scientific measurement of the duration of one day, but rather to indicate that the creation days are not qualitatively different from subsequent earth days. From a phenomenological perspective, an observer placed on the surface of the earth during the 6 days would have seen a cycle of one period of light and one period of darkness just like how he would have expected it to be seen in the subsequent earth days.
There are indeed differences between those with a "clock orientation" and those with an "interactive orientation." Yet, the differences are exaggerated if one thinks that those with an "interactive orientation" have no recognition of time. They do! The difference is how they perceive time should be utilized. Furthermore, all societies most certainly have a basic "clock orientation" in the recognition of the passing of days and nights, if only for the fact that one has to sleep at night and wake up in the morning! So while there are indeed difference in time perception and utilization, it is simply wrong to think that such differences would allow for the stretching of a day to any duration even to millions of years. Sure, one can plus/minus a few hours per day, but that would not have really helped any other position besides the literal 6-24 view.
Poythress attempts to make the duration of a day more indeterminate by appeal to the fact that there was no sun or moon in the first three days, so those three days should not be taken as normal calendar days (Ibid., 141). But that is erroneous, for just because the sun and moon and astral bodies are to function as normal time keepers does not imply that time before the fourth day can be of any length. When God created the light on Day 1, and separated the light from the darkness, time could function already if one sees the light as shining from one direction onto a rotating earth. Moreover, there is no indication in the text that the first 3 days were meant to be in any sense qualitatively different from the next 3 days, so this argument is invalid.
So in conclusion, yes, there are indeed difference in the perception of time between different societies. Yet, those difference are overblown if one thinks that it would allow for the duration of a creation day to be stretched indefinitely. So while Poythress' point about perceptions of time might be helpful to those who are dogmatic about it being scientifically 24 hours, it is little relevance for those who are more interested in the day being a normal calendar day, who use "24" as a short-hand to indicate their view.