A new vote on Prime Minister Theresa May's divorce deal - which lawmakers have already rejected twice - is likely next week, when those same lawmakers will have to decide whether to back a deal they feel does not offer a clean break from the European Union, or accept that Brexit could be watered down or even thwarted by a lengthy delay.
The main motion was backed by MPs from across the various political parties, however most Conservative MPs voted against the motion. A handful of Conservatives are unlikely ever to be satisfied but she may draw in a small number of opposition Labour lawmakers.
However, Ms Rudd abstained from voting.
On Wednesday, MPs voted on two amendments before a government amendment ruling out a no-deal Brexit.
She has warned that extending the departure date beyond three months could harm trust in democracy - and mean that the United Kingdom would have to take part in May's European Parliament elections.
This is the date May has given for an exit under her deal.
The votes were the last in a series of vital parliamentary decisions on Brexit over several days, mean that Britain's departure from the European Union should not now take place before June 30 and gave May a window to resuscitate her plan.
A bigger delay would also see Britain take part in European Parliament elections in May - bizarrely re-immersing the country in EU politics after Brexit was originally meant to have gone into effect.More news: Lori Loughlin's daughter leaves yacht owned by ... USC chairman
The European Commission said the bloc would consider any request, "taking into account the reasons for and duration of a possible extension". May's decision to offer a free vote on an issue where there are "strong views on all sides of the debate".
"The responsibility for delay is exclusively with my Brexiteer colleagues who did not vote for the deal, and have delayed the process further. As a delay was passed by Parliament, I want to see deal agreed ASAP so we can minimize to short, technical, extension".
Following the top level discussions, DUP deputy leader Nigel Dodds said: "We have had a long series of discussions with a series of Cabinet ministers today". If the extension is approved by the European Union there can still be a "no-deal" Brexit if no agreement is reached by the new deadline.
And former cabinet minister Esther McVey - who resigned her role over Mrs May's Brexit deal - also suggested she might vote in favour of it.
HAMPSTEAD and Kilburn MP Tulip Siddiq defied the Labour party whip today (Thursday) and voted for a second referendum on Brexit.
The government narrowly survived an attempt to give lawmakers control of the parliamentary agenda on March 20 with the aim of forcing a discussion of alternative Brexit options at a later date.
It revealed that leader Jeremy Corbyn and senior aides have met with backbenchers Peter Kyle and Phil Wilson, who are promoting a plan to accept Mrs May's deal on the condition that it is subject to a second referendum. We would need at least a year. To take no deal off the table, it is not enough to vote against no deal - you have to agree to a deal.
"It would give a long reflection period for the British political system to look at how they want to approach Brexit again", he said.
"Let us, as a House of Commons, work now to find a solution to deal with the crisis facing the country and the deep concerns that many people have for their livelihood, for their lives, their future, their jobs, their communities and their factories", he said.