There are two words in the English language that might go all but extinct in the near future: 'Eurosceptic' and 'Europhile' (plus their various synonyms). If a 'Eurosceptic' is somebody who wants to leave the European Union, and if a 'Europhile' is somebody who wants to stay inside, then Brexit will render both terms obsolete. My guess is that the uneasily coalitions, which these two terms have come to denote, will now split three ways.
On one end, we will get what you could call the Hotel California coalition, the people who will seek to keep Britain in the EU in spite of the referendum result. They will argue that people do not 'really' want to leave the EU, even if they said so at the ballot box. People were being tricked by the Leave campaign, they were being misled by the tabloid press, or they were just venting their frustration at other things. This is the line taken by, for example, Laurie Penny in the New Statesman:
"This was never a referendum on the EU. It was a referendum on the modern world, and [...] the frightened, parochial lizard-brain of Britain voted out, out, out".
The Hotel California coalition will either try to secure a rerun of the referendum, or a premature general election, which they will then want to turn into a referendum by proxy. Or they will argue that the referendum was just a big public consultation exercise, the result of which should be 'thoroughly looked into', i.e. ignored. You can check out any time you like, but you can never leave.
At the other end, we will get a 'Leave Means Leave' coalition, consisting of people who will want to stretch the referendum mandate to the absolute limit. The truth is that 'out' is not one single status, but a broad spectrum. Even after Brexit, we will, of course, still cooperate with the EU in a lot of ways. But how close should that relationship be? Does 'out' mean 'far, far out', or just 'at a safe distance'?
The Leave campaign implied that after Brexit, the UK could remain part of the single market, whilst opting out of the free movement of people. Unsurprisingly, European leaders are now making clear that that option is not on the cards. Non-EU countries can be part of the single market, but only if they also accept freedom of movement - the 'Norway option' or 'EFTA/EEA option'. If the EU's position does not change - and it probably will not - the Leave-Means-Leave coalition will insist on ending free movement nonetheless, even if this means sacrificing the UK's access to the single market. The people have spoken, they will say, and the people have rejected free movement. The coalition will be led by people like Dr Liam Fox MP, who already made clear:
"I do not believe there is room for membership of the single market, if it entails free movement of people. Those who voted to leave the EU would regard it as a betrayal [...] We do not need to be part of the single market"
This is where a third coalition could come into play, and unlike the other two, it is so far a hypothetical one: Team Norway. It could consist of pragmatic Remainers, who accept the referendum outcome, and who are now looking for a second-best solution, and of liberal Leavers, who are in favour of free movement, or who at least see it as a price worth paying for single market access. This would be by far the most troublesome coalition, even if their positions are perfectly compatible, and perfectly consistent. Team Norway would be made up of people who have thus far been on opposite sides of the divide. They would find themselves with new bedfellows they do not quite trust, whilst coming under fire from their respective former allies.
But this coalition, if it can be formed, would offer the best way forward. A Norway-type deal would immediately end the extreme uncertainty surrounding Brexit. Try googling "What will Brexit mean for...", or something along those lines, and you will see hundreds of questions coming up, and no, they are not just about whether the UK will still take part in the Eurovision song contest. "It will be more or less like in Norway" is a reasonably reassuring answer. "We cannot tell you the details yet, but we will try to secure a bespoke deal, which may take years to negotiate, and which we may not get in the end" - not really.
But a Norway deal is more than a quick fix. What virtually all forecasts, which predicted negative economic consequences from Brexit, had in common, was the assumption that a post-Brexit Britain would be outside of the single market. A Norway-type deal would invalidate them at a stroke.
The alternative to a Norway deal would be continued delays and continued uncertainty, probably followed by an acrimonious split, and the return of intra-European trade barriers. To avoid this, proponents of the single market must now put their differences aside, and work together. Regardless of whether they were once Eurosceptics or Europhiles.