Most media commentary on Brexit makes a huge mistake. It focuses on what the UK government may wish to do or should do. The first stage agreement told us one thing that we should have known the moment Article 50 was triggered: the EU is calling the shots in these negotiations.  But the fact that the UK agreed to the text, and particularly the parts on the Irish border, has told the EU something important: the current UK government is not going to walk away with no deal, and even if it did the current parliament would almost certainly stop it.
That in turn tells the EU that it can get, to the first approximation, the agreement it wants. So what we should be asking is not what the UK’s next move will be, but what the preferred outcome for the EU is. My guess would be that their preferred outcome is a formalisation of the transition arrangements. This satisfies their three criteria: it avoids a hard Irish border, it imposes no additional trade restrictions, and the UK is clearly worse off as a result of leaving (because it has no control over the rules it must obey).
As Martin Sandbu points out, the first criteria could be satisfied by a deal that kept the UK in the Customs Union and Single Market for goods, but not for services. As the UK exports more services than it imports to/from the EU, the EU’s second criteria might still be roughly satisfied by such a deal. If the UK avoids accepting free movement as part of the deal, whether the third criteria is satisfied becomes debatable. Still it would be a possibility. Anything beyond this would mean a hard border in Ireland. It is difficult to imagine why the rest of the EU would want to seriously harm relations with Ireland by agreeing to such a thing.
Suppose something between these two alternatives, of staying in the Single Market and staying in it just for goods, does become the final deal. I think the Labour leadership could live with it if they are in government when the deal is done. Perhaps a majority of Conservative MPs could. But it means that dreams of doing trade deals with other countries would no longer be possible, and for that and other reasons a large part of the Conservative party would not be happy. The Conservative’s Europe problem would not be solved.
The fact that the Brexiters will still be agitating for a more pronounced break from Europe will be one reason why the UK will still suffer in economic terms (albeit much less than with No Deal), and this will be increased if we are no longer in the Single Market for services. Firms will always be reluctant to locate in the UK because trade might be disrupted if the Brexiters win again. Less immigration from the EU will also hurt the economy. And of course the Brexiters will remind everyone that the UK is having to accept rules on trade that it plays no part in creating.
All that suggests any deal will not be sustainable in the longer term. Norway and Switzerland may be able to tolerate being out of the club but obeying its rules because they would probably reason their impact within the club would be small, although what Ireland will achieve with the Brexit deal is a counterexample. An economy with the size and more importantly the history of the UK will find that more difficult to accept this.
Does this mean that any deal will just be the first stage of breaking away from Europe? The Brexiters will agitate for this, but I doubt it will happen. The Brexit is essentially a project of the old. It seems far more likely to me that as time passes a majority for rejoining will emerge, and Brexit will come to an end. This mad period of UK politics, and all the political and economic harm it has done, will be a complete dead end, a colossal and damaging waste of time.
This is my best guess at how Brexit will end, although I take no pleasure in that.  Not with the bang of a second referendum or a parliamentary vote, but slowly over time. The vote that rules them all today will gradually be seen not as the liberation and empowerment that so many now believe, but instead as just the machinations of a small number of hollow men. Hollow men who dream of empire renewed, and as a result are casting their country from the world stage. Hollow men who dream of personal power, and who instead turn out to be powerless. Their day will soon pass, as wind in dry grass.
 Here I think informed analysis, from commentators like David Allen Green for example, got it right. As I wrote: "Anyone who actually wants a good deal from the EU when we leave should realise that the UK’s negotiating position becomes instantly weaker once Article 50 is triggered."
 The Brexiters will not let the government propose a second referendum. A majority of MPs will not vote for one unless public opinion becomes much more anti-Brexit. Without something like a major recession, which looks unlikely, I fear a shift in public opinion will not happen in time for 2019. The post-Brexit Remain campaign has not ‘broken through’ because the tabloid press, and broadcasters following the wishes of politicians, will see Brexit through to completion because they made Brexit possible.
Would things be different if Labour campaigned for a second referendum? In terms of public opinion, that would make a difference to how broadcasters treated the issue. But Corbyn will only consider that if he could be sure that enough Conservative would back him, and by making the issue party political he cannot be sure of that. It is the fact that too few Conservative MPs are prepared to stand up against their leadership, and the 'will of the people', that makes leaving inevitable.