I've been thinking about how divisive various possible outcomes would be (they all would), and I think the magnitude would be a combination of the level of 'betrayal' and the level of 'impact'.
Betrayal being that the outcome is not what people voted for. Impact being the effect on people's lives and the length of the continuation of uncertainty.
So lets look at possible outcomes without a second referendum.
Remain - massively high on 'betrayal', but low on 'impact' - life would return to a level of normality immediately and would continue in that vein.
No deal - high on 'betrayal' - both remainers and many leave voters would rightly feel betrayed that this was never a suggested outcome in 2016. Impact - massively high, all bets are off on the immediate and medium/long term impact of crashing out in March without a deal - the shock would be felt for years, perhaps decades. Potential existential threat to UK with risk of both NI and Scotland leaving.
May's deal - medium on 'betrayal' - many brexit voters feel passionately that it isn't really brexit and that 'it wasn't what we voted for'. Impact high - continued uncertainty as the real issues are kicked down the road for after the withdrawal agreement ends. Would result in brief respite as we transition into withdrawal agreement, but then the same arguments over Norway vs WTO vs cake and eat it, vs backstop etc start all over again. Potential existential threat to UK with risk of both NI and Scotland leaving.
Those are not the only options.
May's deal getting voted down will result in another scramble for Norway\something else and I've just listened to Barry Gardiner say they will not go for another referendum at that time but instead go back to the EU.
Scotland or NI leaving isn't a threat, Scotland's electorate thinks its more left than rUK so they have valid case to leave rUK.
NI needs a border poll and that isn't likely anytime soon, but if they wanted to leave the principle of self determination is fine.
Just imagine if Scotland voted yes in their independence referendum but their Parliament went back to the people because they couldn't get a good deal from rUK, there would be uproar.
There is always division perhaps that is the wrong word, disenfranchised better, a effecting large section of the population, the hard right returns.....