Except, Crimson, from interviews with Leave voters it was very clear that most of them had their own vision of how Brexit was going to happen, and that's what they were voting for. The Leave campaign promised a version of Brexit which the EU was never going to give them, and that's what a lot of Leave voters expected. I imagine the number of people who supported Brexit at any cost are a fairly small portion of the electorate, mostly the kinds of people who voted UKIP in parliamentary elections.
I think it's fair to say that you have a hell of a lot of people who would have voted "Remain" if they'd known the only options were May's deal or no deal, rather than the deal Leave promised or whatever other perfect deal they had in their heads. OTOH, you also have Remainers who think that bridges with the EU are so thoroughly scorched it's not worth trying to salvage. (I might be one of them if I were a UK citizen.) I'd suspect the former group considerably outnumbers the latter, but either way, the way you find out is through a vote.
In normal circumstances, it would be ideal to have a new parliamentary election instead of a new referendum, but the problem is that Euroscepticism cross-cuts party lines in the UK, yet May and Corbyn both support Leave and are whipping their parties to vote with them. Wales and Scotland both have major local pro-Remain parties, but voters in England don't have an option besides the Lib Dems and this new group, both of which will have a hard time winning new seats in a FPTP system even if they enter an electoral alliance. (Remain voters in NI are in a similarly difficult position, because the two main parties are the Eurosceptic DUP and the abstentionist Sinn Fein.) The position Remain voters and MPs are in now is basically the situation that Eurosceptic voters had before the referendum, except on a ticking timeline.
Now, I'm someone who thought the first referendum was a bad idea, but I also think that if you're going to hold a referendum on the abstract concept, you should probably also hold one on the actual deal. It's absolutely ridiculous to insist on treating a five percent margin in a nonbinding referendum on an unnegotiated deal as the final word on Brexit because "the people have spoken," and then insist that the people don't get to change their minds when they know the actual deal.