No, that doesn't seem to be even possible in the solar system as it is now. Especially asteroid impacts - there have been no impacts large enough to make humans extinct within the last several billion years.
Dinosaurs extinction events, yes. But they didn't have our technology. Many of us would survive an impact like that with some warning (as we would certainly have for a 10 km asteroid). Just protection from firestorms, shelter, food, and other things we have with our technology could have saved mammals of our size at the time of the dinosaurs - and stockpiles of food to last through the cold years to follow.
But what's more, we are already close to mapping all the asteroids of any size in the inner solar system. Already we know ALL THE TEN KILOMETER NEOS out to the outer asteroid belt and beyond. And we have found 90% of the ones of one kilometer or larger and find a new one every month, expect to get to 99% by the 2020s.
So a big asteroid would have about ten or twenty years of warning as it would be in an orbit from beyond Jupiter.
I think this idea that we need a backup in space - though it has several eminent people behind it - is totally misguided. Even brilliant people sometimes make mistakes.
After all there is nothing in nearby space anyway that is anywhere as habitable as Earth - even immediately after a large asteroid impact. Not going to be hit by something so large it removes Earth's atmosphere and oceans. And the atmosphere and ocean by itself make Earth far more habitable than anywhere else in our solar system.
And that big impact they worry about is only a one in ten million chance for the next century.
One big enough to make Earth uninhabitable - not likely in less than several hundred million years.
We can use space technology yes. That does give us an edge here.
But, instead of trying to run away from a disaster that probably won't happen for half a billion to a billion years - we can put a tiny fraction of that funding into speeding up the search for small asteroids in our solar system.
And that way we can predict any potential impacts. Though chances are there aren't any dinosaur ending type ones - not of ten kilometer or larger objects - it's already 99.9999% certain we don't find anything that big on a trajectory to hit Earth in the next century.
But if we do, with plenty of warning, we can deflect it. And we are likely to find at least a few of the very small ones as they hit Earth every few decades, and very small ones still large enough to detect and track if we have the funding, down to 20 meters - they hit Earth even more frequently. We can practice deflecting those or just evacuate the impact zone. And may find one that is headed towards a city and deflect it. And so learn by "baby steps" scale up so we are ready if we ever need to deflect a really big one in the future.
That surely makes more sense. See my science blog posts:
We could learn new things about life from Mars, and could be of huge positive benefit to humanity, potentially. But I think more from the discoveries we make there, than as a place to live. And it would be tragic if in a rush to runaway from a disaster that never happens, we end up messing up another planet as well as Earth.