Video report by Political Correspondent Carl Dinnen
There will be "consequences" if Article 50 is prolonged, the EU has said as Theresa May prepares to ask for an extension.
The comments from the European Union come just hours after Downing Street admitted the UK is "in crisis" over Brexit.
The EU's chief negotiator, Michel Barnier also said that any extension to Britain's membership had to be "useful" and warned it would bring "uncertainty".
Commenting on the length of any potential extension, Mr Barnier said a longer delay would only be granted if it is "linked to something new, a new event, a new political process".
ITV News Political Editor Robert Peston assessed that Mr Barnier's comments imply a general election or referendum would be required in the UK before the EU commits to a longer extension.
In a live broadcast from Parliament, Robert Peston said Downing Street's description that the UK is in "crisis" over Brexit "might be an understatement".
He added: "This is the greatest failure of our Parliamentary and Government system that any of us alive have witnessed."
Watch Robert Peston's most recent Brexit assessment here:
Mr Barnier's announcement comes after the Prime Minister was dealt a massive blow by Speaker John Bercow after he ruled that she would not be able to bring a Withdrawal Agreement before MPs unless it is "significantly different".
Mrs May is now set to write to the European Council asking for an extension of Article 50 ahead of the summit in Brussels on Thursday.
A spokesperson for Mrs May said: "In the PM’s speech before [the second meaningful vote] she said if MPs don’t support the deal 'we would be in a crisis' and yesterday’s events show that has come to pass.”
Ahead of an expected extension appeal from Mrs May, Mr Barnier said: "The EU authorities want to know what the underlying political process which would be the grounds for that extension would be - political process within the House of Commons or in the general political debate in the UK.
"It is our duty to ask whether this extension would be useful because an extension will be something which would extend uncertainty and uncertainty costs."
He added: "What would be the purpose and the outcome of an extension and how could we be sure that at the end of a possible extension we are not back in the same situation as today?"
Meanwhile, Brexit Secretary Stephen Barclay indicated ministers will continue to press on with Theresa May's Brexit deal despite Speaker John Bercow's Commons ruling.
Mr Barclay said Cabinet would give "serious consideration" to Mr Bercow's decision that the Government cannot bring the deal back for a third "meaningful vote" without substantial changes.
However he said the Speaker had made clear in earlier rulings that the Commons should not necessarily be bound by precedent.
The Speaker’s ruling, announced in an unexpected statement to the Commons, throws a further obstacle in the way of the Prime Minister’s scramble to get a deal agreed by the scheduled date of Brexit of March 29.
John Bercow sidestepped questions about his ruling as he bought a coffee on the way to Westminster on Tuesday morning
A Government source said it seems “clear that the Speaker’s motive here is to rule out an MV (meaningful vote) this week which also stands in the way of a securing a shorter extension”.
“[This] leads you to believe what he really wants is a longer extension, where Parliament will take over the process and force a softer form of Brexit.
“But anyone who thinks that this makes no-deal more likely is mistaken - the Speaker wouldn’t have done it if it did.”
Solicitor General Robert Buckland - one of the Government's legal advisers - said the Government was facing a “major constitutional crisis” and Mr Bercow’s intervention would have “huge reverberations” for the Brexit process.
Boris Johnson refused to answer questions following a meeting with the Prime Minister
Meanwhile, Labour leader Jeremy Corbyn said an extension to Article 50 until the end of June at least "gives time for a discussion" and added that he has already spoken to the EU about his proposals, which they said could form a basis for negotiations.
He claimed the Government is in "chaos" and said if it "can't get a majority for its way on Monday" then "surely that is the time to step aside and let the people decide on a People's Vote and it's called a general election".
He earlier met with members of the “Norway Plus” group of MPs on Tuesday in which they affirmed they were all opposed to Mrs May's deal, or a no-deal Brexit, and would push for a second referendum is the Prime Minister forced her deal through Parliament with "threats and phoney bribes".
Mr Corbyn met with SNP Westminster leader Ian Blackford, Lib Dem leader Sir Vince Cable, Plaid Cymru MP Liz Saville Roberts and Green Party MP Caroline Lucas to hold talks breaking the current Brexit deadlock.
A spokesperson for the Labour Party said the leaders all "affirmed their common opposition to the government's botched deal or a no deal outcome.
"Should there not be a majority in Parliament for May's deal or a public vote, Corbyn called on the other parties to engage constructively to find a Parliamentary majority for a close economic relationship with the EU that can work for the whole country.
"The party leaders discussed efforts to ensure May's deal would be put to a public vote if she is able to force it through parliament with threats and phoney bribes."
Meanwhile in Dublin, European Council President Donald Tusk held talks with Irish premier Leo Varadkar to discuss the backstop arrangement which both the EU and Ireland insist is necessary to keep the border open.
In a joint statement, they said Mr Tusk had expressed "strong and ongoing solidarity" with Ireland and they had agreed they needed to see what proposals would now emerge from London.