Well I did say a compromise in my second line, there can be ways to buy more time (or for that matter, lose it). Does depend on how strict the timer is anyway, I'm assuming some worst case where the developer badly misjudges how long the majority will take and people end up in a blind rush to finish the game and ignoring content.
But then again, Fallout did it well, rush to get the WC and then ta-da : new antagonist.