Unfortunately, while Parliament has said there shouldn't be a No Deal, that remains the default outcome if we come to a deadline with no agreement to a deal and no extension. Unless of course Parliament compels Article 50 to be revoked - which we can't depend on it doing.

A public vote, either a referendum or a General Election, seems the only way out. Even if Labour were to sign up to a deal with May, there is no reason to think it would be any more likely to be approved by the Commons. More Labour MPs might vote for it, but fewer Tories would.