LONDON - British Prime Minister Theresa May launched her mission Tuesday to attempt to rescue her Brexit deal with a round of meetings with European Union (EU) member leaders.

Political commentators described it as a mission impossible after Brussels indicated it would not alter the deal already agreed between the EU and May's government.

Jean-Claude Juncker, president of the European Commission, said in Strasbourg there is no room whatsoever for renegotiating the Brexit deal.

At Westminster a lengthy debate, won by the main opposition leader, Labour's Jeremy Corbyn, was expected to be highly critical of the way May handled the crisis on Monday by postponing a parliamentary vote on her deal.

With no date set for MPs to vote, politicians fear it could roll over into the early weeks of 2019. Downing Street said at a briefing Tuesday that MPs will get to vote on the Brexit deal "before January 21".

That date is seen as the deadline for a decision to give enough time to complete the process in the Houses of Parliament ahead of the March, 2019 departure date when Britain leaves the bloc.

As the pound remained at a low level Tuesday, Dr. Mike Ellington, a finance expert at the University of Liverpool, told Xinhua that further depreciation later on in the week would show financial markets have no faith in May's announcements to address MP's concerns regarding the current Brexit proposal.

"In other words, she has lost her credibility and there is absolutely no point in kicking the [Brexit] can down the road any longer," he said.

Ellington added that over the medium-longer term, in light of the current proposal being rejected, Britain can fully expect to see increases in measures of economic policy uncertainty. This, he warned could ultimately lead to contractions in GDP growth and recession through a depletion in business confidence and investment.

He told Xinhua: "I cannot see the EU agreeing to a new outline exit deal and the decision to hold off the vote suggests maybe Theresa May is coming to realize that any Brexit deal is inferior to the current status quo. In my view, the best thing to do is to get the MP vote over and done with so we can move forward."

May is pinning her hopes of getting clearer assurances from EU about the fate of the border issue between Northern Ireland and Ireland.

Although both Britain and the EU say they do not want to see the border return, if the backstop is implemented it would need approval from Brussels to remove it, potentially locking Britain into following EU rules indefinitely.

It has that fear that has led to MPs of all parties, particularly Northern Ireland politicians, from refusing to accept May's deal.

Juncker added in comments there was room for further clarifications on the deal, but commentators warned that may not be enough to win over critical MPs at Westminster.

He told the European Parliament Tuesday the withdrawal agreement was the best and only deal possible.

He added: "There is no room whatsoever for renegotiation but of course there is room, if used intelligently, to give further clarifications and interpretations without opening the withdrawal agreement. Everybody has to know the withdrawal agreement will not be reopened."

In a radio interview Tuesday, the Leader of the House of Commons Andrea Leadsom said May was seeking to give the British Parliament a vote on whether to enter the backstop, and an annual vote on whether the country should remain in it. She said May was absolutely determined to get a deal Parliament can vote for.

The thought of a backstop has infuriated the Democratic Unionist Party (DUP) who have an arrangement to support May's minority government to give her a majority.

In her keynote speeches on Brexit, May has constantly said that no British prime minister, including herself, would agree to a deal that involved different trading arrangements in any part of Britain, including Northern Ireland.

Britain's national newspapers Tuesday gave their verdicts, with a range of critical headlines. The Daily Mail headlined "May's last roll of the dice", saying facing a humiliating defeat she was forced into a dramatic climbdown. The Guardian's front page said "Desperate May reveals her plan B -- to buy more time".