If I'm wrong, can you provide evidence that we have all the capabilities that you claim? I find it hard to believe we're at all prepared for potential cataclysmic situations.
The wide range of environments in which algae thrive is something any biologist could tell you.
The availability of electric generation capacity, and the prices thereof, is a matter of public knowledge. The fact that coal burning is still cheaper than many "renewable" power sources is a contingent if not trivial fact. Any human on a greater than subsistence income who wanted to use only solar power, could.
Of course, asking for proof that we're "prepared for potential cataclysmic situations" is the mother of all goalpost maneuvers.
It's hard to believe only if you understand it as "everybody would be fine". A cataclysm would probably kill or starve many people, but what is hard to believe is that there would be no survivor at all.
Consider a nuclear submarine for instance. This facility is capable of remaining totally autonomous during half-a-year (it even produces its own oxygen). It's not too hard to imagine that something similar could protect a fair amount of men and women from basically anything, and for a longer period, if it only is modified to do so.
Consider also this non-exhaustive list of underground bunkers: http://io9.com/the-secret-world-of-underground-bunkers-51160... You could probably store enough food and other resources to survive during decades in these. Certainly enough time to figure out how to eventually survive outside, regardless of what exactly happened there.
And finally, remember that there are already thousands of survivalists all over the world, actively preparing for the end-of-the-world.
What is hard to believe is that a few environmental factors would cause the death of absolutely all human beings on Earth.
