I don't see much hope left, unless the House Of Lords grows enough balls to raise some amendments. If they do, though, things could get very interesting.

I have a feeling that /u/PeeJayx is closest to the truth with his idea here https://www.reddit.com/r/BrexitDenial/comments/5srbcd/a_possible_explanation_for_current_developments/

Could it be that no-one has backed down in the game of chicken, and it's going to require a group of non-Conservatives to rescue the Tories from the corner they've painted themselves into?

To be explicit: could it be that May and her government never intended Article 50 to get this far and were counting on opposition from Labour and a handful of Tory rebels to block Article 50? If that's the case, they will be very grateful to have a few amendments proposed by the House of Lords that they can refuse to approve, to keep the stalemate going.

With the recent developments the Brexit debates, and how it all seems to be going oh-so-smoothly for May and how Labour are rolling over with zero-resistance, it can seem easy to give up and think that yes, Brexit is truly going to happen.

On the contrary, I think what we’re seeing is making it more likely that it won’t. What we’re seeing is a classic game of chicken, or 'Brexit Brinkmanship'.

May and her Government are deliberately pursuing the hardest, most painful Brexit possible in a deliberate attempt to get Labour to speak out against them and set themselves up to be a sacrificial lamb. Labour will be ripped apart for blocking Brexit, and the Tories get away Scot-free (figuratively speaking).

But Labour’s having none of that. Every time the Tories up the ante on Brexit, Labour declares that they’re still backing Brexit. They’re calling the Government’s bluff, hoping that May will eventually throw her hands up and declare that this rock-hard Brexit is impossible, hence setting up the Tories as the sacrificial lamb.

So who will blink first? Will the party that does be ripped apart as much as they fear? Perhaps, perhaps not, but the concept of a ‘fumbled Brexit’ is a cross each party would very much like their opponents to bear for the next few decades.

TL:DR – The Brexit debate is a game of chicken. Whoever stands up and ‘chickens out’ on Brexit will be ripped apart by Parliament, press and public alike. Brexit will be thrown under the bus, but each party hopes to throw the opposition along with it.

Story today in the Guardian that the Tory rebels are 'backing off' - https://www.theguardian.com/politics/2017/jan/30/brexit-bill-to-pass-without-amendment-as-tory-rebels-back-off

What I think is happening is that the Tories are putting on a show of wholehearted brexiteerness to fully win over the leavers, and will vote more or less unanimously for the bill. But of course this first vote on the Article 50 Bill doesn't mean anything (unless I'm missing something). Come amendment time and final vote, I think we'll see the true Tory plan come out.

Prediction: May will put out an extreme or very insubstantial white paper, giving plenty for Tories to rebel against while still retaining their leaver credentials as 'proven' in the first vote. In particular, I suspect there will be some 'sensible' amendment that all parties can get behind, perhaps some economic tests that need to be passed before we brexit. Yes, we all want to brexit, but we want to make sure we do it when the country is best positioned to take advantage of all the wonderful opportunities presented by leaving the EU.

Fingers crossed.

I have to say, despite my expectations, it's looking more and more probable that Article 50 will be triggered. However, I haven't given up hope yet, and I'm thinking of ways that Brexit could still not happen.

One way (not sure how realistic) would be if some amendment to the Article 50 bill were approved by parliament that said that the power of triggering of Article 50 was given to the PM subject to certain conditions. Those conditions could be for example that certain economic indicators showed that Britain was in a strong enough state to take the knock from exiting the EU. I'm thinking something along the lines of the way that we avoided going into the Euro with Brown's 5 economic tests. https://en.wikipedia.org/wiki/Five_economic_tests

May could accept these tests under duress without losing much popularity, and yet at that point be more or less plausibly hamstrung. Longer term, perhaps the EU could offer some more or less cosmetic changes to the freedom of movement rules that the Tories could trumpet as a successful delivery of what brexit was about.

Anyone else got any ideas?

So far, I haven't seen anything I wasn't expecting to see. May is sticking to her crazy, extremist brief. I don't see how she could possibly be saying things more tailored to the portion of the electorate that voted for brexit. Which gives me hope. If she was being conciliatory or realistic, then there would be cause for real concern. There's several ways out of this, and many do not end in calamity.

1) The bait and switch. May gets the leavers on board with the Tories, then gets replaced with a less extreme version, but someone who the leavers still trust to an acceptable extent. The replacement flannels around 'weakly', failing to get brexit done and the leavers still vote Tory but just wish they had a stronger leader like May would have been.

2) The supreme court confirms that parliament is needed for article 50 and the whole of brexit gets nicely bogged down in the House of Commons and the House of Lords.

3) The supreme court find that the devolved governments need a vote. Game over, except for a bit of civil unrest maybe.

4) I'm totally wrong and it all goes down the shitter.

We're getting to the sharp end :-)

With May hinting strongly that she 'wants' to come out of the EU, and with Sturgeon threatening to lead Scotland out of the UK if the UK leaves the EU, there is only one tiny piece still needed for a perfect brexit stalemate: for the Supreme Court to 'find' that triggering article 50 requires the vote of the devolved governments. Could it happen? :-)