Johnson in particular is a very divisive figure in the parliamentary party.
If the deal is not passed, and no other course of action can be agreed on, the default option would be that Britain crashes out of the European Union without a deal. The House of Commons carved out time for legislators to hold a series of "indicative votes" on alternatives to May's defeated deal.
Some prominent opponents, including former Foreign Secretary Boris Johnson, quickly said they would back the Brexit agreement, but Northern Ireland's Democratic Unionist Party said it remained opposed because of concern that the deal treats the region differently from other parts of the United Kingdom.
"Theresa May's pledge to Tory MPs to stand down if they vote for her deal shows once and for all that her chaotic Brexit negotiations have been about party management, not principles or the public interest", said Labour Leader Jeremy Corbyn. But it still faces long odds.
In a last-ditch bid to win over opponents in her Conservative Party, May announced Wednesday that she would step down if the deal is approved and Britain leaves the European Union.
If lawmakers seem unified around the idea of May's departure, nothing else is certain.
A more flexible politician might have decided at that time that a minority position in Parliament would require reaching out to others for something as divisive as a Brexit deal, but May opted to go it alone.
Following two hefty defeats for her deal, she's offered her premiership in return for getting the necessary support for her plan.
If the parliamentary vote does not take place, May will have to spell out to European Union leaders what steps Britain will take by a deadline of April 12, or risk crashing out of the bloc without any arrangements in place.
The country has been in political chaos since June 2016, when it passed a referendum to leave the EU.
Johnson said on Tuesday evening that the current agreement with the European Union was a "terrible deal", but indicated he would be prepared to back it so long as "the second phase of the negotiations will be different from the first".
"She put her case well, and reiterated that she had done her duty", he said.
Importantly, it remains unclear whether MPs will be instructed to vote along party lines or with their conscience when alternatives are put to them.
The British government had already agreed, under worldwide law, with the European Union (EU) for an extension to quitting the regional bloc until at least April 12.
Lawmakers will vote at 3 p.m. ET on a ballot paper for as many proposals as they wish. House of Commons Speaker John Bercow said he would not accept another vote on the twice-rejected deal unless substantial changes were made.
While May's departure would not alter the terms of the Withdrawal Agreement, it could give Conservative eurosceptics who have opposed it a greater say in negotiating the terms of Britain's future relationship with the EU.
It looked like it might not be enough, as a key Northern Ireland party said it would not be supporting the deal.
Britain could otherwise seek an even longer extension that puts it in the odd situation of having to take part in European Parliament elections almost 2 months after it was supposed to have left.
"They may feel they are not sufficiently represented by the UK Parliament but they must feel that are represented by you in this chamber".
Britain's Electoral Commission has budgeted for European elections and could hold them at short notice but Mrs May has said it would be "unacceptable" to take that route.