Faced with the reality of living in a mine for the rest of their lives, no-one who is keen on colonising Mars would actually then sign up for it. Who would agree to basically imprison themselves on the off-chance of being the seed of a new humanity if the earth is made uninhabitable (an already unlikely proposition)?

Humans live in a ridiculous variety of environments as it is - an extinction event would have to be utterly catastrophic to wipe out all breeding populations.