See there's a bit of a problem there from the perspective of both gameplay and narrative.
For a time limit to work, it needs to be immediate and it needs to be active. This is why time limits work for, say, clear this platformer stage in X seconds, finish this one-on-one fight in a fighting game in X seconds. Or the clear objective "find the Water Chip in 30 days". These are relevant, immediate, and tangible time limits that contribute to the moment because set the goal to reach and the sense of accomplishment from reaching it. The water chip is easy to find well before the time limit is even close, but it adds to the sense of triumph in the first act of the game.
A time limit that's a distant and abstract concept (like for instance the second time limit in Fallout) is NOT such a time limit. It doesn't feel like it impacts your game directly. What it feels like is an external force taking the game away from you and saying you can't play anymore. IIRC the second time limit and possible alterations to it (the water merchants from Hub) aren't actually even mentioned in Fallout, which also reduces the value of the limit in every respect because it does not set a visible goal which is the only reason to have a time limit. But even if it did, it's far far too long to possess any relevant value for the moment because it is so far away and vague (again, contrast to the 30 days where the day or two of traveling after the rat cave is just right for giving it a sense of immediacy and urgency). This also doesn't quite contribute in any meaningful way to the threat of the super mutants because the super mutants as a threat are very low-key, you barely meet them during the game and barely hear about them. You never for instance see a place that super mutants have conquered and dragged off everyone from. All of these are only post-mortems end scrolls for the game. So you have a threat that is obscure and never seen directly, with a time limit that is too long to give any sense of hurry.
This leaves the second time limit in Fallout an abstract and arbitrary thing that serves no purpose and has no value. The only saving grace it has is that Fallout is a much shorter game than the second time limit.