Here are some possible scenarios:
Back to parliament
May must submit a new plan for Britain's next steps by the end of January 21. It is not clear what her "Plan B" is, but some local media have reported she would ask parliament to vote again on the deal, perhaps after seeking another set of reassurances from the EU.
Some MPs have floated the idea that parliament could, in a temporary break from convention in Britain, take control of the process away from the government and hand it to a committee of senior MPs from across the political spectrum.
It is not clear that this plan is technically possible, or whether it has enough support to succeed. The government said any attempt to prevent it from meeting its legal obligation to deliver an orderly EU exit would be extremely concerning.
Will Theresa May resign?
May could resign as leader of the Conservative Party, triggering an internal contest to replace her without a general election.
Should she choose this option, the party will look for a new leadership. This will either be contested — a process that could take up to eight weeks — or appointed by acclamation if the other candidates were to back out.
It's unclear whether May can survive, having lost such a crucial piece of legislation by such a wide margin.
That said, May defeated an attempt to oust her as leader of the Conservative Party in December, winning a confidence vote by 200 votes to 117. The result means her position as leader of the party cannot be challenged for 12 months.
Vote of no confidence
The opposition Labour Party said it will call a vote of no confidence in the government if May's deal is rejected, but did not specify exactly when.
If a majority of MPs vote against May's government, Labour would have 14 days to prove, by a vote, that it could command a majority and form its own government. That would allow Labour to take control of the country without an election.
But Sky News notes a defeat for May is not a foregone conclusion. Tory MPs are unlikely to vote against her, knowing this could trigger an election and ultimately see them lose their own seats.
If May was to win the motion, she would continue in office for the time being. If she lost, she would come under immense pressure to resign.
If no government is formed, the nation goes to the polls.
Back to the ballot
If May's government loses a confidence vote and Labour is unable to form a new government, an election is called. She could also call a general election herself if two-thirds of MPs in parliament agree to it.
But as The Australian notes, this would not be a good look. For one thing, it would require two-thirds support of the parliament.
But also, May is wary of voter fury, with the electorate increasingly frustrated with fighting among Tory MPs.
May has previously said that a general election is not in the national interest.
Second referendum
The route to a second referendum on Brexit — or a People's Vote — is unclear.
But unless the plan to give control of the process to parliament is successful, it would require the backing of the government of the day. A new referendum can be called only if it is approved by parliament.
With May deadset against a second referendum, and the opposition Labour Party not committed to one (but not ruling one out), a second referendum would need either a change in Prime Minister, a change in government or an abrupt change in policy.
An increasingly vocal contingent of MPs from across the political spectrum supports a fresh vote to break the impasse in parliament. But, so far they have not been able to prove there is a majority in parliament for this view.
Even if parliament did agree in principle to a second referendum, Britain would then have to ask for an extension to its timetable for leaving the EU.
Delay or cancel Brexit
The government could seek to extend the negotiating period with the EU to give it time to try to reach a better deal, hold a general election, or conduct a second referendum.
An extension of Article 50 — the legal process that triggered the two-year time limit for Britain to finalise the deal — has been gaining traction in recent weeks. But the EU would have to sign off on this.
The government could also withdraw its notice of intention to leave the EU, which the European Court of Justice has ruled it can do without consent of other EU countries.
May has said she does not want to delay Britain's exit from the EU, and will not revoke the notice of intention to leave.
