There is precedent for a second referendum - Ireland did so in 2009 on accepting the 28th Amendment. I admit, this is a lot bigger.
I think the context here which may help this to make more sense to those outside: a lot of British people voted for leave on false claims. Ok, lots of elections have false claims. But these were enormously misleading and widely spread. It seems like there are a lot who regret their decision, though I'm not sure what % they represent. If there is a general election called early with a party that explicitly backs EU membership winning, then there's no way we can leave without another referendum. And if we vote to stay, I think there would be grounds for the EU to get us to accept a lot of things which we might not have before.
But yes, it's a totally miserable situation for everyone.. you know what, I'd even say it's miserable for the politicians who 'won'.