A small colony on Mars won't survive without Earth any more than the Vikings survived in Greenland without trade from Europe. Read Jarad Diamond's COLLAPSE if you want to understand what destroys civilizations.
Even if the vast majority of us die in the process and we're left with a global population of just 1B or 500M, then that is still enough for a decent civilization capable of supporting space flight; on the other hand, a risk that threatens to destroy us permanently is far more important than a risk that'd simply harm us, and from which we'd be able to recover in time.
The goal is not a small colony of Mars - such a colony is simply an investment & testground to become a multi-planet species, which also is the only way how we can mitigate all risks that may cause Earth to become uninhabitable - including climate change, nuclear/biological/whatever war, asteroid strikes etc.
This is a side note, but I was actually just looking at population growth over time, and it kinda blew my mind that the estimated global population was only 310m 1000 years ago, and 879m 200 years ago. The idea of losing ~93% of the world's population sounds catastrophic, but given our current medical technology (and a post-apocalyptic "mandate" to reproduce and repopulate the earth) I don't think it would take us very long (relatively speaking) to recover. Kinda crazy.
No responsible scientist can come out and predict this because it is unknown territory. But if you want to go to Mars based on a meteor-driven event at the P-T transition, you damn well better worry that we recreating the events that lead to the 'Great Dying' at the end of the Permian that took out 90% of all _species_ at the time.