Lightning Returns: Final Fantasy XIII can go past 13 days, but it's a secret
In the trailer released last week for Lightning Returns: Final Fantasy XIII, it's stated that there's 13 days left until the end of the world. Siliconera reported earlier on a Gengeki PlayStation feature that talks about how players will travel across Lightning Returns: Final Fantasy XIII's vast world. Basically, there's two ways: you can get around on foot or by monorail (if you want to get around faster). "Por favor manténganse alejado de las puertas."
Apparently, in Lightning Returns, the game can be extended beyond 13 days. In Final Fantasy XIII, one day was 26 hours. After the events of XIII, two hours were lost, bringing a day in Lightning Returns to 24 hours. While there's a 13 day limit to save the world, it is possible to extend Lightning Returns past that limit, but Square Enix says it's a secret.
It's worth noting that test players have been finishing the game between two and four days. There's not a lot of change to the ending based on how long it takes you to beat the game, but there are things you can experience depending on the time-based system. What does this mean exactly? I have no clue, but it sounds like I'll be playing it multiple times to see what changes with differing playthrough lengths.