Do I actually only have 3 days to save Miller?

So, I got to Chapter One, and Ocelot kept talking about he thinks Miller "probably has about 3 days left". This seems like an arbitrary number he chose.

When I finally got control of my character, I listened to all the audio tapes I'd unlocked and noticed that about 6 hours of game time had passed in the 20 or so minutes I'd been listening to them.

This made me wonder... am I actually under a time constraint to save Miller, or can I run around and explore as much as I want before proceeding with my main objective?

If you wait long enough, the mission will fail when you rescue Miller, ending in a Time Paradox.