The current deal is such a bad deal that the ruling government suffered the worst loss in modern Parliamentary history when they submitted it for a vote. That has tell you something right there.
The truth is that the majority of the MPs would likely support it, it’s just that many of them don’t want to be on the hook for supporting it because then they would have to justify that support to the voters in the runup to the general elections in 2022. That is not going to go over well in a lot of districts. So they’re trying to defy the wishes of the people without being seen as doing so. How to square that circle? For starters, they’ve been voting against all alternatives to May’s deal and they’re hoping May can get a more palatable deal from the EU that won’t look so bad to the voters. But the EU likes the deal as is and thinks the MPs can be intimidated into voting for it after all when it comes up again next week. Big game of chicken there.
I think the MPs reject the deal again, but they’ll also vote against No Deal the next day. So then they will vote for an extension in order to avoid leaving with No Deal. One downside to the extension for the EU is that if the extension lasts long enough, they’ll have to permit the UK to send representatives to the EU Parliament in the elections taking place this May.
A second referendum won’t happen, the fight over the wording would be too ferocious to get it off the ground and there is no guarantee the government will get what it wants out of that vote given that the sentiment hasn’t gone away.