Well, at least somebody has a plan.
An extension requires unanimous consent of the 27 EU countries. The EU leadership has taken the position that they would only consider an extension if the UK got its act together and had a concrete plan that just needed time to implement. Not happening.
There is a vote to block a no deal Brexit tomorrow, which is expected to pass.
The key question is how blocking a no deal Brexit will be implemented, given the rejection of the withdrawal agreement (not a deal!) and the reluctance of the EU to extend the Article 50 period without something different such as a general election or people's vote. There is also the upcoming European Parliament elections in 3 months which -- if the UK stays past that point -- the UK would need to participate in if Article 50 was extended past that point.
A general election is also problematic as it will likely result in another hung parlaiment or slim majority and we will be back where we are. This is especially the case given that Scotland is overwhelmingly SNP, and may gain seats over the Conservatives/Tories.
While a people's vote may be a potential way out of the deadlock, the government (and maybe the majority of parliament) are against it. Even if there is a majority for it, there isn't a majority for what to ask in the new vote. There are MPs that don't want remain on the vote, and there are others that don't want no deal on the vote.
I would guess that if a majority of MPs voted against a hard Brexit, that would imply their for an extension. If that were taken off the table it would be logical (ha!) to conclude that they would support an article 50 reset. Of course the rest of the EU also know all this, so they don't really gain much from pushing the UK to that option.