1)How do you get to a referendum 2. Every time the tories the move towards something of soft brexit they lose part of their vote to UKIP, Labour need the labour voters who voted leave to have any chance of getting into government. So while yes we could say that it's strong leadership for May or Corbyn to openly go for a second referendum/people vote, if all it does is make a media shit storm for a few weeks, destroys your party chance of being in government and also destroying any influence you could have on Brexit then I'm sure how what kind of leadership that is.
The remain argument only works if there's overwhelm feeling of wanting to remain and at the moment there simply isn't that feeling. I mean most people in the Wales & England are willing to give the North of Ireland back to the Republic(Cheers lads it was never yours in the first place) .
2)For another referendum it would have to pass in parliament, would it even get enough votes ?
3)The Lib Dems have for sometime being a pro remain second referendum party are so far in polling they haven't got more than 10%.
It's just a really shit situation.
If people want the softest version of Brexit then they will have to vote for Labour. But if people want Labour to become a remain/2nd referendum party then they'll have to do what the left did and take over the party membership and vote for Pro Remain leader.