"We're probably overdue for some such calamity in our own civilization...."
I agree 100%
I agree 100%
I'd bet very heavily against it. Even Velikovsky and his followers never tried to claim that cosmic disasters were likely in our own times. In fact, if memory serves, Velikovsky claimed that the incidents of short-period comets, volcanism, and earthquakes, the three most major lingering effects of recent catastrophes (according to his theory) had been damping exponentially since Roman times and that with every year which goes by, the odds of anything like that happening again decrease significantly. Again if memory serves that was in "Earth in Upheaval".
According to that view cosmic mishaps aren't something which happens randomly every million years or so but something which we saw a whole lot of about 3000 years ago but which there is about zero chance of happening again in the forseeable future.
On the other hand if you go with traditional theories, then you don't really figure it's time again after 65 million years; more likely you take the mean time between such incidents (70 million years or whatever) and divide by half, and you'd figure the next such event was about 30 million years in the future, starting from today.
I'm not losing any sleep over it.