London (CNN) Former British Prime Minister Harold Wilson once famously opined that a week was a long time in politics. For today's incumbent, Theresa May, the past 24 hours must have felt even longer.

When May traveled to Brussels on Monday, it was in the expectation that she would sign a historic agreement with European Union leaders that would enable Brexit talks to move on to a crucial new stage -- the nature of a future relationship between Europe and the UK.

The timetable was tight: The remaining 27 EU nations are set to meet on December 14 and 15 to decide if "sufficient progress" has been made to move on to the second phase of negotiations. Even though Britain doesn't leave the EU until 2019, businesses want clarity now so they can make crucial investment decisions.

So the choreography was set: a working lunch with European Commission President Jean-Claude Juncker, followed by a meeting with European Council President Donald Tusk and capped off with a triumphant statement to the House of Commons in London on Tuesday.

It didn't quite work out like that. May relies for support in the UK Parliament from a small but hardline party in Northern Ireland -- the Democratic Unionist Party (DUP). And when the DUP's 10 members of Parliament got wind of the language in May's deal around the arcane but historically significant issue of the Irish border, they had something of a public meltdown. May was forced to abandon her plans and return to London.

May insisted later that there were merely a "couple of issues" that remained outstanding and that she was confident a deal could be done soon. But as the dust settled on Tuesday, it was clear from the previous day's breakneck developments in London, Brussels and Dublin that the contours of a final Brexit deal had fundamentally changed.

What's on the table?

When Brexit negotiations began just under six months ago, the EU was clear on its position: It would not countenance any discussion about a future relationship with Britain until "sufficient progress" had been made on three issues: that Britain pay a substantial "divorce bill;" that rights of European citizens in the UK are guaranteed; and that there is no reinstatement of a border infrastructure between Northern Ireland, which will leave the EU with the rest of Britain in March 2019, and the Irish republic, which remains in the EU.

After tortuous negotiations, the two sides were close on the first two issues, in particular after the UK agreed to make a substantial payment to the EU budget, leaving the Irish border as the final stumbling block.

It is a historically delicate issue: The dismantling of border controls and infrastructure was a key plank of the Good Friday Agreement, which brought peace to Northern Ireland after years of sectarian conflict.

Finally, on Monday morning, negotiators appeared to have found common ground. The UK would guarantee that Northern Ireland would continue to be aligned with EU laws and regulations that, if they diverged, would require checks at the border.

Unfortunately for May, the text leaked. Members of the DUP -- which devotes its entire energy to preserving the union between Britain and Northern Ireland and opposes any suggestion that its laws and regulations could be hitched to those of Dublin -- were furious.

JUST WATCHED Brexit showdown bringing uncertainty to UK Replay More Videos ... MUST WATCH Brexit showdown bringing uncertainty to UK 01:48

May was forced to return to London and try to placate the DUP.

Her calculation appears to be that the DUP will fall in line. After all, can the party afford to risk the £1.5 billion funding deal for Northern Ireland that it struck with May upon agreeing to support her government?

And if the DUP withdrew its support from May and left the possibility open for another general election, would it risk the election of the Labour Party and its leader, Jeremy Corbyn, becoming Prime Minister? Corbyn has in the past expressed support for Irish nationalist causes, anathema to the DUP.

So if she can get past her problems with the DUP, what are the options for May? Unfortunately for her, all are replete with problems.

Soft Brexit

What is it? Under a so-called soft Brexit, the UK would remain in or closely aligned with the EU's customs union and single market. It would ensure that the UK would adhere closely to EU rules and standards, although it would not have a say in how they were agreed on.

Why could it work? Such a stance would be well received in Scotland, Wales and London, whose leaders have already backed it. Most large business leaders would welcome a close relationship with the EU. A "soft Brexit" template already exists: four non-EU countries participate in the single market through membership of the European Free Trade Association.

Why might it fail? Critics will accuse the government of betraying the people who voted to leave, with this deal effectively allowing the UK to remain in the EU. It would also rile the Brexiters in the Conservative Party who would likely protest against the deal.

May's majority in Parliament is thin and she cannot afford to alienate members of her own party without risking a vote of no confidence. In any case, she has already ruled out this option and it seems unlikely that she would reverse course.

Hard Brexit

What is it? A hard Brexit involves cutting as many ties with the EU as possible while maintaining some form of trading relationship. It's what the most ardent supporters of leaving the EU demanded -- that Britain "takes back control" of its laws and immigration policies. It would require negotiators to conclude a tailor-made trade deal, and is the most complicated of all the options: It took nine years to forge a trade agreement with Canada.

Why might it work? It would please the hardcore Brexiters as it would take the UK out of the customs union and single market while also ensuring the country had full autonomy over its legal system. The option has support from some senior figures in May's cabinet and a small but vocal section of her MPs.

Why might it fail? If the UK leaves the customs union and single market, it's hard to see how customs checks would not be required at the Irish border, and a hard border wouldn't pass muster with the government in Dublin. It also seems likely that such an option would not command a majority of votes in the House of Commons.

Irish Taoiseach (Prime Minister) Leo Varadkar wants the UK to make guarantees over the border between Northern Ireland and the Irish republic.

No deal

What is it? If talks collapse, and Britain ends up without a trade deal or even a transition arrangement, the logical legal consequence of Britain triggering the Article 50 process of leaving the EU means that it would crash out on March 29, 2019.

Why might it work? In the absence of bespoke trade deals, there is a ready-made framework for world trade: the terms agreed on by the World Trade Organization. Many countries in the world successfully trade with each other on WTO terms.

Why might it fail? Theresa May used to insist that "no deal is better than a bad deal," but most business leaders believe WTO terms would be disastrous for British trade. In any case, WTO rules don't cover some crucial areas of pan-European cooperation, such as on security and aviation. It's also highly unlikely MPs would approve leaving the EU without a deal.

Staying in the EU

What is it? If neither "soft" nor "hard" Brexit can command sufficient support in Parliament, and if MPs refuse to allow a "no-deal" Brexit, the only other option would appear to be remaining in the EU.

Why might it work? Most legal experts believe the UK could suspend the process of leaving the EU if it wants to. EU leaders have said they would prefer the UK to remain in the bloc. Most business leaders believe leaving the EU would be economically disadvantageous.

Why might it fail? Even the most ardent pro-Remain politicians generally accept that Britain is leaving the EU, and the debate is merely about how close a future relationship would be. But the Brexit process has been nothing if not unpredictable, and if no other option is on the table, there is at least a theoretical path to Britain remaining in the EU.

British Prime Minister Theresa May (L) and European Council President Donald Tusk are hoping to strike a deal.

What will happen now?

The European Commission has made it clear that it believes a deal was done. The Irish government's position is the same. The clock is ticking: EU officials say an agreement must be made within days if the UK wants a European summit on December 14 and 15 to agree to move on to trade talks.

But all sides are prepared to give May time to square off the 10 MPs of the Democratic Unionist Party. "The show is now in London," one official said.

Speaking to reporters in Brussels on Tuesday, British Chancellor Philip Hammond insisted he was "very confident" that there would be movement over the coming days. "We have made a lot of progress over the last weeks," he told reporters. "We have made tremendous steps forward. We are very close, but we are not there yet."