The deadline the EU has imposed means that no deal is now much more likely than before. I think there is little or no chance of May's deal being passed. The deadline then gives Parliament a couple of weeks to assemble a majority for something like Norway+ or to revoke Article 50 or to let no deal exit happen. I would still make Norway+ the slight favourite of the three but it's now much tighter because of time limitations. So assuming May's deal is voted down there's three options.
Leave without a deal. The Tory Party will split with half the cabinet resigning, the People's vote campaigners will be incandescent with a lot of their ire directed at the Labour Party.
Revoke Article 50. This would produce a split in both parties (because a lot of Tories would vote for it and a significant number of Labour MPs would vote against) but particularly again in the Tory party with half the cabinet resigning (just the other half). The Leave Means Leave voters would be incandescent with most of their ire being directed at the Tory MPs who had voted for the revocation (there would have to be a significant number for it to get a majority).
A majority asks for something like a Norway+ deal and asks the EU for a longer extension to work out the details. This would involve big splits in both parties. It might involve forming a temporary national government. It would certainly mean a new PM and because of the need to assemble a cross party majority I think some kind of national coalition would be quite likely.
In all three cases there will be major splits in the existing parties and new much more coherent alliances will have formed. In other words the realignment will have taken effect quite quickly and within Parliament, as it did in 1886. It will then find expression in the world outside Westminster - I think with possibilities 1 and 2 you would see the emergence of what would effectively or actually be a new party.
The EU can decide what happens now. I get the feeling that quite apart from thinking they are fed up with May and le total bollocks some of them (particularly Macron) are now coming to the conclusion that a clean break is better for both sides in the long run, not least because they have other fish to fry, to put it mildly. I think there is certainly a feeling that they no longer want the UK in the EU with politics here in its present state as we would be a seriously disruptive force in various ways. That might push them to saying "No, you've voted down the deal you had, exit for you now". Alternatively they would go along with a Norway deal (which is what they really wanted in the first place) if they think there is a sufficiently large majority in Parliament to get it through and that majority is stable.