Jeremy Wright will be the first to put forward arguments in the four-day hearing, while lawyers for pro-parliament activists who won their argument at the High Court last month are set to start speaking tomorrow afternoon.
"The government’s case is that it does have legal power to trigger Article 50 on the timetable set out by the Prime Minister," said Wright, in a statement issued ahead of today's hearing. "We do not believe another Act of Parliament is necessary."
Jeremy Brier, a barrister at Essex Court Chambers, told City A.M. the government's skeleton arguments for the Supreme Court looked "much more persuasive and confident [than last time]....it looks more like it's game on".
Meanwhile, speculation is mounting that the government is already preparing a short Brexit bill. Tightly worded legislation could allow Theresa May to stick to her March deadline for triggering Article 50, regardless of which way judges rule.
A Brexit department spokesman declined to comment directly on whether such legislation was being prepared, but added they were now focused on the Supreme Court appeal and hoped the judges would overturn the earlier decision.
"In the event that it doesn't, we will assess precisely what remedy the Supreme Court requires and will set out our approach at that point," the spokesman added.
Brexit-backer and top Tory Steve Baker told City A.M. he was confident neither the House of Commons nor the Lords would prove obstructive.
Former attorney general and Remain campaigner Dominic Grieve told City A.M.: "I think it would be certain to go through. There would perhaps be attempts to attach amendments to it, and there would likely be some general debate, but I'm pretty clear that something like this would go through regardless."
Precisely what legislation could be needed to trigger Article 50 is still unclear. Supreme Court judge Lady Brenda Hale found herself under fire last month after suggesting that if the judges did not decide in favour of government it could delay the triggering of Article 50, as the new law required could prove to be complex.
Such a delay could renew uncertainty and be a blow for businesses. Two hundred business leaders, including both Leavers and Remainers, have already clubbed together to urge the Prime Minister to stick to her Article 50 timetable and are due to deliver a letter saying as much today.
Daniel Hodson, executive committee chairman of the Financial Services Negotiation Forum and coordinator of the letter, told City A.M. businesses were keen for the Brexit process to begin, so they could draw a line under at least one element of uncertainty.
Labour leader Jeremy Corbyn has already vowed to seek amendments to any Article 50 legislation, telling Sky News this weekend the party wants assurances on “market access and protections” while a handful of Labour representatives, including London MPs David Lammy and Catherine West, have said they will vote against any Brexit process regardless.
Lib Dem leader Tim Farron told City A.M.: “We will try and amend the bill, and if necessary, we will do this by proposing extra clauses to it to ensure proper debate and scrutiny of the process and the issues.”
Nonetheless, the Lib Dems also admit they are unlikely to be able to rally the numbers to block the triggering of Article 50.
Today's hearing has attracted massive international interest, with nearly 100 reporters expected from around the world. The courtroom will also be more crowded than the initial hearing as a number of intervening parties, including Scotland's lord advocate and the counsel general for Wales, have joined the case. In addition, two further cases, both concerning Northern Ireland, have also been tacked on to proceedings.
Meanwhile, a statement from David Greene, senior partner of Edwin Coe, who is acting for one of the respondents, Deir Dos Santos, noted the court has made special arrangements to accommodate security guards for those involved. This follows reports that the lead claimant on the original case, Gina Miller, has spent over £60,000 on personal security since taking the government to court earlier this year.