I posted elsewhere about this, with a list of the likely effects of such an asteroid. Short answer is no, they wouldn't have the slightest chance of surviving.
They almost certainly wouldn't survive even the initial shock wave, even in the titanium-lined basement. But if they did, the potential fireball/ mile-high tsunami(s)/ earth-buckling earthquakes/ burning poisonous gases/ lack of oxygen/ destruction of all plant & animal life (i.e., all future food sources)/ decades-long incredibly cold winter would most certainly kill them.
A 70-mile asteroid would be an extinction level event. Virtually all land life larger than bacteria would be extinguished. A vast amount of the ocean's life would be extinguished as well.
About the only (remote) hope for any humans to survive long-term would be a massive underground complex in a high mountain with years if not decades worth of food, enough stored fuel to generating years if not decades worth of power and light, quite possibly decades worth of breathable air, and some kind of system that would prevent energy generation from poisoning the air they had to breathe. You would also have to somehow preserve any seeds, plants and animals for future crops and food supply. All of this just to keep say a hundred humans alive.
I don't know that such a system would be possible even with the entire might and money of the US government and years to prepare.
Fortunately no object this size has hit the earth for billions of years.
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