I heard once in a recording of R' Moshe Wolfson that when the verse in Tehillim (93:1) says אף תכון תבל בל תמוט - [Hashem] set up the world that it not tilt - that this implies that the world cannot be destroyed by our actions. To me, this makes a lot of sense, as if we believe that Hashem made the world with a Divine purpose and mission, would He allow that to be subverted by something as inconsequential as people not recycling enough? The world won't be destroyed or become uninhabitable through our actions.
On the other hand, micro impacts could very well happen, and the world could become a less pleasant place to live, whether it be some minor degree of global warming or whatever the case may be that would cause small scale disasters. This has indeed happened in places where there were nuclear meltdowns or smog, for example. Therefore, it does not seem necessary for our survival to take care of our environment, but it could very well be that it is in our own best interests to maintain a pleasant environment.