Many experts think that a Norwegian-style deal with the EU would be the least worst version of Brexit. Under this arrangement the UK would leave the EU but join the European Economic Area (EEA). The advantages are that this would guarantee access to the single market, cut our net contribution to the EU budget while allowing the UK to take control of agriculture and fisheries (areas which most people accept need serious reform). It would also allow the UK to cut trade deals with third countries.
Of course, we would still have to obey most EU laws (while having little control over them), and accept freedom of movement. Nonetheless on paper at least this looks like a way to respect the wishes of the majority, while minimising the harm and disruption to the economy. The big question is whether such a deal will be palatable to the British public. To answer that question I asked Anthony Wells, the director of political and social research at YouGov, and highly respected online pollster. YouGov's eve-of-election forecast of a very narrow Remain victory, although incorrect, was closer to reality than the majority of polls.
However, in practice such a deal would be hard for Theresa May to sell to her party, as it "would be seen as a betrayal". Indeed, his gut feeling is that most of the Conservative Party, especially in parliament, "oppose anything that could be seen as a fudge" (exit polls suggest that Conservative Party members voted to Leave). If she wants to guarantee support for continued access to the single market "she would need to move very quickly to take advantage of her honeymoon", so the fact that "she has shied away from a quick exit would make things a lot harder if she wants to go down that route in the future".
However, Wells notes that "public opinion is not set in stone". Indeed, if there is a recession, "public attitudes could swing much more strongly in favour of remaining in Europe". Indeed, he notes that it would be "almost impossible" to predict the outcome of a second vote (whether on the EEA or even full membership) in advance. The classic case was the 2011 referendum on the alternative vote, which in his view ended up boiling down to the question, "do you want to give Nick Clegg a slap?"
Incidentally, Wells thinks that Cameron's big mistake was to "overplay the economic arguments against leaving", which were successfully dismissed by the Leave campaign as "Project Fear". Although they were supported by a lot of evidence, the way in which they were delivered turned "a potentially winning hand into a liability". Of course, Wells admits that, "a wholly positive campaign wouldn't have worked either", given Britain's lack of enthusiasm about the EU. So it's fair to say that the now former PM faced a difficult balancing task, which he handled badly.
A Brexit-related economic downturn could also shift sentiment north of the border. After the vote, Wells expected renewed demands for Scotland to leave the UK, since it voted overwhelmingly to stay in the EU. To his surprise this hasn't been reflected in his company's polling on the topic, which has found "no move toward Scottish independence so far". However, Wells warns that if the economy worsens then this could quickly change. Similarly, if oil prices rebound from around $50/barrel, then the Scots could become much more open towards leaving Britain.
Finally, Wells notes that the European public is generally hostile to a deal, especially one that doesn't involve freedom of movement. Indeed, they clearly think, "that Britain doesn't deserve any special favours". However, the treatment of the UK may not be a major factor in next year's elections in France and Germany, giving Brussels some leeway to make compromises. Of course, whether it wants to is another question entirely.