Prime Minister of the United Kingdom (UK) Boris Johnson gives a press conference at European Parliament on October 17, 2019 in Brussels, Belgium.Jean Catuffe | Getty Images News | Getty ImagesBritish Prime Minister Boris Johnson has insisted that he is “very confident” the House of Commons will support his Brexit deal on Saturday, in what is widely expected to be a historic knife-edge vote. The former London mayor secured a draft Brexit deal with the European Union on Thursday, following successive days of late-night talks and almost three years of tense discussions. Johnson must now persuade a majority of U.K. lawmakers to support the draft agreement if he is to take Britain out of the EU on Oct. 31 — something he has promised to deliver “do or die, come what may.” Saturday’s showdown is likely to be framed as a “new deal or no deal” moment, with the prime minister acutely aware it will be his last chance to get Members of Parliament (MPs) to approve the deal before the Brexit deadline. However, the parliamentary arithmetic looks daunting for Johnson after he agreed to strike a deal with the world’s largest trading bloc without the backing of the Northern Irish Democratic Unionist Party (DUP). The DUP, which supports Johnson’s government on a confidence and supply basis, has said it will be unable to support the deal on Saturday. “A narrow defeat in Saturday’s Commons vote on Prime Minister Boris Johnson’s Brexit deal is now our central scenario,” Mujtaba Rahman, managing director of Europe at Eurasia Group, said in a research note published Thursday. ‘Real prospect of a humiliating defeat’ Among other issues, the DUP has said it will oppose Johnson’s draft deal over concessions made by the U.K. to the EU on customs checks at points of entry into Northern Ireland. “As things stand, he faces a real prospect of a humiliating defeat because the DUP’s 10 MPs are refusing to support his deal,” Rahman said.He added that while Johnson is “gambling” the DUP will drop its opposition to his deal, there was no sign of this happening before Saturday’s vote. That’s because “the agreement would deny Unionists a veto when the Northern Ireland Assembly voted every four years on whether the province should remain in the EU’s regulatory and customs orbit, with an effective border in the Irish Sea.”In the absence of support from the DUP, it is likely Johnson will need to count on the support of the 21 Conservative MPs he expelled from the party last month as well as some opposition Labour lawmakers.’It is going to be tight'”Johnson has a chance, but it is going to be tight,” Kallum Pickering, senior economist at Berenberg Bank, said in a research note published Thursday.The winning post in the House of Commons is 320, assuming everyone turns up to vote for Saturday’s extraordinary session. Seven Sinn Fein MPs do not sit and the Speaker and three deputies do not vote. Presently, there are 287 voting Conservative MPs, and Johnson will need to limit any rebellion among them. Pickering estimates 283 will back Johnson’s new Brexit deal, thus leaving the prime minister needing 37 from outside his own ranks.A pedestrian walks up a staircase on the southern bank of the River Thames with Houses of Parliament seen in the background in London on September 2, 2019.TOLGA AKMEN | AFP | Getty ImagesThe prime minister “can probably count on the 21 MPs whom he kicked out of the parliamentary party in the last two months to back the deal on the basis they are brought back into the party,” Pickering said. But, that would leave the prime minister 16 votes short of a majority. Earlier this year, when Johnson’s predecessor Theresa May took her own Brexit deal to MPs — for what turned out to be the third and final time — a total of nine lawmakers (five from Labour and four independents) backed the prime minister. Pickering said that even if they, and the suspended Conservative MP Charlie Elphicke, now back Johnson’s deal, it would still leave him six votes short of a majority.