Yes, it is distinctly strange when the argument against a second referendum is that asking the people what they think now is deeply undemocratic and undermines "the will of the people", irrespective of what the "will of the people" is now that it's clearer what we're getting ourselves into (and certain campaign promises have evaporated ...). The Greeks, who invented democracy, often re-voted and changed their minds. I also seem to recall Theresa May putting her deal to the vote multiple times in the hopes of getting it through. Johnson is doing the same in his attempt to get a pre-deadline election.
I guess a more reasonable argument against a second referendum would be that, with the country essentially split down the middle, a second referendum is likely to yield another marginal result that is, say, 51.9% in favour of staying (whereas the previous one was 51.9% in favour of leaving), and thereafter calls for a third referendum would arise (or for a "best of three") and so on ...
Looking at opinion polls, although staying in has consistently been more popular than leaving for the past two years, there's still not an awful lot in it, and if the polls are right, likely what you'd get would indeed be a marginal victory for staying in the EU (though there's no guarantee that polls give an accurate prediction in terms of who'd actually come out and vote). Opinion may have shifted a little, but it doesn't look like there's been an overwhelming change of heart, I think.
I'd say positions have become become increasingly polarised and unlikely to change all that much in the face of facts, reasoned argument and statistical likelihoods, all of which can easily be dismissed as lies and fake news (by either side), and often are. Especially given how complicated the whole situation is and how much is unknown. Witness, for example Rees-Mogg's ad hominem dismissal the concerns of a doctor who compiled the government's own report on the impact of a no deal Brexit on the supply of critical drugs and medicines. Mogg's argument was simply that the doctor was a "remoaner" and this was more "Project Fear".
A referendum could help settle what the "will of the people" is on the no deal situation. Currently it can be argued that, since the referendum result was to leave, we should leave at any cost. Conversely, it can be argued that when people voted for leave, they weren't voting for no deal, but to leave with the promised advantageous deal we were told that we'd easily get from EU. Had they specifically been asked about leaving without a deal, they'd have voted differently.
Various polls have consistently shown the British public would prefer to stay in the EU to leaving without a deal, and the margins here are bigger than above, typically staying is around 10 percentage points ahead (often around 45% versus 35%). If this were replicated in a referendum, the argument that leaving without a deal was fulfilling "the will of the people" would be much harder to make.
That said,
another (one-off) poll suggest the majority (52% to 38%) want it over and done with by 31st October whether there's a deal or not. So, maybe that's the will of the people too. And yet another (one-off) poll suggest the public are split almost exactly 50:50 on the question of whether it's worth extended negotiations til January 2020 to avoid a no deal. Both polls can't be right.