One could argue that they didn't expect the vote to pass at all, and did it to gain favor with their constituency - to be able to say they "tried to leave the EU but alas." They knew their promises were untenable, yet they made them anyway, but there's no way to fulfill them once the vote passes, hence resignation.
The leave voters will just complain, but it avoids all the chaos and cost associated with leaving, when there's no clear benefits.
I seriously think that UK should stop the process and start again. This is not undemocratic because people now know better (new circumstances justifying a re-evaluation). The process would be like this:
1. The parliament decides to cancel the process
2. A Spanish judge made a proposal how to halt the Brexit
3. An emergency committee tries to find a temporary deal with the EU
4. After a year or so, the popular vote is repeated
They aren't stupid. They knew all along it would be impossible. They didn't think the vote would go for brexit. They wanted to use it as political leverage and they underestimated the stupidity and malleability of the public and the powerful amplifying influence of social media.
They resigned.
Boris Johnson the Foreign Secretary resigned. David Davis who was literally the "Brexit minister" resigned.
https://www.washingtonpost.com/world/europe/theresa-mays-gov...
Here are more people who resigned.
https://news.sky.com/story/the-ministers-who-have-quit-over-...
My view is that these people lied to the public about how awesome Brexit would be. Once it got to the hard work of making it happen they realized how awful the deal would be and how the economy would be harmed. Because they didn't want their name attached to it they resigned.
Some of them are hoping that May will resign and they can become Prime Minister instead.