Yeah, essentially "extremely possible" is just "far from impossible". Something can be very possible but still not very likely, surely?
I'd never come across anyone using this phrase until Nate Silver did. Is it a US English thing?
It doesn’t mean that a broken heart will definitely kill you, just that there is definitely a chance that it will kill you.
I could totally imagine Nate trying to emphasise the idea that 20% is a much bigger probability than say 1% by using language like that, but put too much weight on it here leading to confusion.