Britain's most senior judges will rule if Theresa May has the power to trigger the formal process for the UK's exit from the European Union.
Ministers are braced for the Supreme Court to decide that Parliament must be given a vote on starting the divorce proceedings.
It follows a legal challenge by the Government after a landmark High Court ruling in November that the Prime Minister did not have the authority to launch Article 50 of the Lisbon Treaty without consulting MPs and peers.
In an unprecedented move, all 11 Supreme Court justices sat as a panel to hear the appeal.
If it rules in favour of the Government, Mrs May has stated she intends to trigger Article 50 by the end of March.
If it upholds the High Court judgment, Parliament will debate and vote on invoking the measure.
The Government wants to stick to its current deadline for starting the process and, if it loses the appeal, is expected to swiftly publish a Bill.
Although is highly unlikely to lose the vote, the progress of the legislation through Parliament could be frustrated.
Labour has said it will table amendments demanding an early "meaningful" vote on the divorce settlement agreed between the UK and EU leaders.
It is calling for Britain's exit package to be renegotiated with Brussels if MPs reject the deal.
The Opposition will also call for a full Brexit plan to be set out in Parliament as well as regular progress updates.
The SNP has said its 54 MPs will vote against the plans if they reach the Commons and the Lib Dems will oppose the move unless the PM promises a second referendum.
Dozens of Labour MPs are also reportedly preparing to vote against the process being launched.
Liberal Democrat leader Tim Farron has called on Jeremy Corbyn to set out if he would compel his MPs to back legislation to formally start the Brexit process.
The Labour leader has said his MPs will not block Article 50 but has refused to say if he would impose a three-line whip requiring them to vote for the measure.
Mr Farron said: "There is nothing progressive about giving Theresa May a blank cheque to decide what form of Brexit she thinks is best and impose it on the country.
"So far, Labour have said they will seek to make amendments to the Bill, but have said they will not vote against it even if they do not secure key amendments - this isn't good enough.
"If Labour believe amendments are needed then surely if they do not pass you should vote against the Bill?"
The legal battle follows the successful High Court action led by businesswoman Gina Miller that blocked Mrs May from using the royal prerogative to launch Britain's exit from the EU without Parliament having a say.
Lawyers have also asked for the devolved administrations in Scotland, Northern Ireland and Wales to be given a say.
Stephen Gethins, the SNP's Europe spokesman, said: "To simply overlook our elected legislatures and the job we have a responsibility to do would be a betrayal of our democratic system and Devolution itself.
"Given the substantial impact a hard Brexit is likely to have on the devolved administrations the UK government must bring forward legislation that will acknowledge and respect the devolved administrations and is backed by a White Paper that outlines the UK government's position and offers some clarity amidst the ongoing chaos."