Earlier in the day, an amendment, tabled by pro-remain Tory backbencher Dominic Grieve, which would give the Prime Minister three days to come up with a "plan B" if she loses her Brexit deal vote next week, was voted through by MPs - meaning defeat for May's government.
There was a major row in the Commons over whether Wednesday´s amendment could even be put to a vote, with Speaker John Bercow apparently disregarding the advice of his own clerk that it could not.
British Prime Minister Theresa May failed to win over the Northern Irish party which props up her government to her Brexit deal on January 9, just hours before lawmakers were due to resume a debate on the divorce accord.
But her spokesman added: "If that were not to take place. we would respond quickly and provide certainty on the way forward".
Hinting at one path of action MPs could try and force the prime minister down, Sir Keir told MPs: "There is a question of the extension of article 50, which may well be inevitable now, given the position that we are in, but of course we can only seek it, because the other 27 [EU member states] have to agree".
After a two week Christmas recess, United Kingdom parliamentarians resumed hostilities on Brexit, with 20 Conservative MPs joining forces with the opposition Labour party and supporting an amendment to the May government's Finance Bill demanding that a "no deal" Brexit be ruled out.
The No 10 source said the Prime Minister had always meant to respond quickly if she loses the vote.
"We are doing everything we can to win the meaningful vote on Tuesday", the source said.
While 70% of MPs from all parties were critical of the May government's handling of the Brexit negotiations, none of the obvious alternatives to her deal agreed with European Union leaders in November were palatable to them either.
Work and Pensions Secretary Amber Rudd said history will take "a dim view" of the PM's Cabinet if it presses ahead with a no-deal Brexit if MPs vote against her agreement next week.
And Downing Street said it was "very surprised" by the Speaker's decision, as it had been advised the motion setting out the timeline for events was unamendable.
Her proposal aims to restrict the government's freedom to use the Finance Bill to make tax changes linked to a no deal Brexit without the "explicit consent" of Parliament.
"It seems clear that May will lose the vote, the only real question is how much does she lose by", Usherwood added. However, pro-European Tories and opposition MPs backed the Speaker's decision. "Obviously she has had a lot of important discussions over the Christmas break with other European leaders and I'm sure she would want to update parliament".
Wednesday´s amendment, which passed by 308 votes to 297, has more weight.
The government needs 318 votes to get a deal through the 650-seat House of Commons, as seven members of Irish nationalist party Sinn Fein do not sit, four Speakers and deputy Speakers do not vote, and the four tellers are not counted.