There's no other conceivable extinction event that could occur "a couple years out". If you're talking climate change, then I agree that's a major problem, but on the order of at least decades.
Plus climate change would have to get pretty incredibly bad for, say, Mars to start looking easier to live on than Earth.
That's the problem with colonization as an Earth back-up—even Antarctica and the Sahara Desert are more livable than any other body in the Solar System, by a long shot. Another Snowball Earth or a heavily desertified Earth would still be preferable to Mars. Throw in a fair amount of radiation, even—still better.
Cuts down significantly on the sorts of events for which a Martian back-up world is preferable to a shelter-in-place strategy.
But if you could go out now and terraform a planet so that when in future you have problems here you have a place to go to that matches the original environment back on earth. And you learn a lot of things about "geo"engineering, the things you cannot try safely at home, which can come in handy to fix any problem back on earth.
We have no ability to terraform anything, let alone a planet, let alone the economics of it ever being feasible. Life isn't a star trek episode. We can't just go and 'terraform now' as you say. We can barely land anything on Mars without a 50% failrate right now. We're talking technology way, way into the future. Hundreds, perhaps thousands, of years.
This is precisely what we don't know. If you're talking averages, then sure it takes decades to observe a meaningful change. However climate change of the sort we're anticipating now isn't about averages. It's about peaks, it's about records, and possibly major shifts in equilibrium.
Basically what we witness so far and will keep on seeing are spikes in all directions of the spectrums (e.g. record high temps, but also record lows; rain in the Death Valley and droughts in formerly wet areas). More critically, what little we've been able to gather on how fast climate eras shift from one to the next, it appears that whereas in-cycle change happens rather slowly (change within an era, because averages), climate era shifts could happen very quickly (because chain of events). We're talking going from a warm era to a glacial one within a few years, sometimes months even. A high speculation is that some thongs might upset the Gulfstream and you'd observe climate evolve from year to year.
Given our limited sky coverage, we can't really rule out killer meteor on the time scale of "a couple of years", or even a couple of hours, though the probability is extremely low (like, sub-1-in-100 million, for the couple of years time frame.)
Still probably higher than extinction from war in the same time frame.
The resources and practically to gently shoving a comet or asteroid out of the way are probably a billion less than building self-sustaining colonies elsewhere. Worse, now we have two planets to defend, not one.
I don't see the "we must migrate now" types saying "lets put migration away for a while so we can better build anti-asteroid solutions and detection systems."
Arguably, we're just a couple launches and deployments of mass drivers away from fixing this issue. This is all known tech that could be deployed relatively quickly. A self-sustaining Martian colony is probably hundreds of years away considering the work it would take to terraform the planet.