I don't think the British public is listening to the politicians on Brexit much, not any more. Rather, the Conservative Members of Parliament are talking pretty much to or, more accurately, at each other and their party members, and that conversation is more about who is going to be the next leader after whatever is going to happen does actually happen.
Meanwhile, Labour MPs are keeping quiet, to the increasing frustration of more and more of their supporters and party members (including me), partly because they don't want to divert attention from the Conservatives tearing each other apart and partly because the party leadership doesn't want to come off the fence and support what most, I am sure, Labour Party members and MPs want -- a referendum with Remain as an option -- before they have to (and in the case of some of the leadership, until they're forced do). The Labour Party is split on the issue, too, cf course, but nowhere near as badly as are the Conservatives.
Meanwhile, I think most people are getting increasingly tired of the politicians an increasingly worried about the consequences of crashing out the EU by accident. I know I am.
I still don't think No Deal is a likely outcome, but I'm very aware that it's one we could stumble into by accident, since everyone's strategy depends on taking it right down to the wire, and that's risky.