TL;DR - Not impossible but probably less than 50% chance.
As I see it now it will be very hard for any government to deliver an actual Brexit through the Houses of Parliament. It is hard to see how the current government could reach a good negotiated outcome with Brussels given the red lines announced about the needing power to make external trade deals combined with the need for a frictionless Irish border and what are the likely red lines of the DUP. On the other hand a no deal exit will bring down the government, whether for an interim coalition, a new election or possibly a referendum on the no deal outcome.
On the other hand it is also fairly hard to see how Brexit could be completely avoided, some scenarios outlined may provide a path to remaining or a very soft exit.
I'll try to set out some scenarios but these are turbulent times and it is pretty much wild guesswork but I want to illustrate how hard it will be for Brexit to actually be delivered.
This isn't actually a big barrier. We could pay if needed.
Tricky if UK are resistant jurisdication of the European Court of Justice but it is quite plausible a solution can be arrived at whether by the Brexiters flexing to allow an agreement or if necessary the Tories getting support from across the Commons.
This is a key component in any Brexit arrangement both because the EU are prioritising it and requireing a solution for a deal but also because the minority Conservative government relies on the DUP for a majority which adds additional redlines around the issue that may block the whole process.
Fundamentally the non-magical solutions to have a frictionless border in Ireland require that Northern Ireland must have a customs union (or even closer union) with the Republic of Ireland. There are several scenarios for this but each is essentially blocked by different redlines or principles.
There is no immediate prospect of this or any sign of demand from the people of Ireland except an occassional crank who gets an immediate column in the UK right wing press. I only include because it is the only response to the Ireland issue I've heard from Brexiters. But they really need to become much more realistic if they want Brexit to actually happen.
2. Reunification (NI joins Ireland in EU)
Almost as unlikely as Irexit, requiring a NI referendum and unacceptable to the DUP and probably the Conservatives even with a majority. I think it is a very unlikely option although potentially possible in the future it can't even be raised when DUP hold the balance of power.
3. UK remain in Customs Union
This would be a plausible and possible solution except for the Conservative red lines around the European Court of Justice and Brexiteer promises and political need to be able to negotiate UK trade deals with the world outside the EU. This means I don't think that the Conservatives can take this option; but a Labour or Lib Dem lead governement could make these choices.
4. Special Status for Northern Ireland - Creative Solution
I have heard proposals for NI to remain in the single market and customs union while Great Britain leaves it. This would mean different laws and regulations to comply with EU rules, and crucially it would place the customs border (including tarriffs) not between NI and the ROI but instead at the airports and ports between Great Britain and NI. This separation of the UK would likely be completely unacceptable to the DUP. Again this means that the current government would not be able to take this option although it could be an option for a future government without a dependency on the DUP could potentially go down this route although it would be tricky to deliver against the wishes of the NI assembly. David Davis effectively ruled this out
No solution available
I really don't see a single option (or any others) that the current UK government could do a deal on with the EU and hold its majority together. If I'm right about this there is actually no possible deal that the current government could do. That leaves us to discuss how either a no-deal Brexit could be delivered or how another government could take power and what they would deliver.
Trade and Regulations
There is a clear trade off between ease of trade with the EU and the taking back control of regulations. However it is more complicated that that because other trade deals the UK may want to do will want us to lift different regulations to allow them to export to us more easily. If the differences between the EU and UK regulations are in any way significant it will require border checks for complicance and make trade harder. There is no easy obvious route through this and the government have not yet explained the approach that they plan to take or even acknowledged the trade offs. Once they do, whatever the approach it will cost support from one side of the Tory party or the other. Anything but the very closest regulatory harmony (in which case why are we leaving as we will essentially be subject to EU regulations without any say in them) will cause major trade problems and cause all the Northern Ireland issues to kick in.
The fact that the Tories haven't yet made any proposals in this area suggests that they don't have an answer that they can sell. Whether they can actually sell a proposal within their own party let alone get the agreement of the EU for it.
So how can Brexit Stall or Fail?
Firstly I think it is clear that the EU is not likely to make major concessions on their key positions, they are flexible in some ways and the UK essentially have choices and trade offs such as between trade and regulatory freedom mentioned above but also in a great many other areas where there is a choice between divergence and a close relationship. When particular choices are forced some people are going to be unhappy. The more these choices are made the more the effects will become clear and consequences will become clear too, jobs wil be lost and costs will be incurred in making alternative regulatory arrangements.
At any point if the Government loses support of the DUP or a dozen Tory MPs decide they can no longer support the government it will fall, likely triggering an election. Now this is a very unappealing option for Tory MPs as the Tories are likely to lose the election and they could lose the whip effectively be deselected so this is nuclear option for them that would cost their jobs and certainly they would at least be remembered unfavourably by many of their party for bringing down the government. They really want an alternative if available, the government softening its position or something else ending it but I would be stunned if there weren't at least 12 Tories amongst the 318 prepared to do what they thought was right to save the country from major damage when it comes to the crunch but they will hope that crunch doesn't come.
An alternative is that those same Tories could force the government into holding a second referendum with the threat of bringing down the government which could avert Brexit. If the deal is looking bad or no deal is looming I think the government may decide that they want to offer a second referendum to avoid being fully responsible for the consequences.
When the government falls might be crucial to the way Brexit is debated and what the Labour position is. Labour's current position is essential as soft a Brexit as possible, in practice likely remaining in single market and customs union and may even extend article 50 for an extended negotiation and transition period (during which the whole of Brexit could be reconsidered if the public wanted). Its also possible that if the election doesn't come for another 6-12 months that Labour will have decided that the Conservatives have blown the Brexit process so badly that the Europeans will not negotiate further and the only realistic option is to remain. But an election is likely to prevent the worst outcomes.
There may also be Tory leadership challenge although it doesn't seem like anybody actually wants the job as most can see how the Brexit is going and don't want to be leading until after Brexit. It could happen and the results are hard to predict but it may be a mechanism either for a change of direction or a switch to a no deal position which could then precipate the election described above.
How could Brexit actually happen?
Unless there is a change from the current May/Davis/Fox direction it is very hard to see how there will be a deal and if no one stops them we could simply crash out with no deal at all in March 2019 to a total catastrophe. There are variants of this where very limited partial deal can be done but it would still need massive borders and customs changes, huge costs, lost business and trade damage. It also remains to be seen if the DUP could be kept on board when the hard border is being constructed.
One variant path would be similar but the government might flinch seeing the impending damage (and their likely blame) and find a mechanism to be forced into another referendum, the result of which isn't a foregone conclusion. I don't think remain has the ground organisation or data. It isn't yet certain that remain would win although I hope it would be more obvious by then.
An alternative route is that the government largely cave on their negotiating position and switch tack to Norway style Brexit, staying in single market and customs union at least for the next few years. Whether this would bring the governemnt down would depend on the hardline brexiters and what they saw as the alternative (no Brexit and or Labour might be thought worse). A similar outcome could be achieved by a Labour government if there is another election soon.
None of these paths is easy and I think they would all fail for different reasons (with the possible exception of a Labour government soon).
There are easier routes to avoid Brexit than there are to achieve it. My current view is that Brexit won't happen because this government can't deliver it but it does reply on shifting public opinion to enable to it actually be stopped. We need to keep the pressure on.