And senior British ministers have urged May to overcome his inability to pass the eurosceptics into his own party by inviting opposition leader Jeremy Corbyn for talks in order to agree a joint Brexit plan if Parliament votes its agreement
In the meantime, two of the biggest donors of the Brexit campaign say they now believe that the project they eventually support will be abandoned by the government and the United Kingdom will remain in the European Union.
Peter Hargreaves, the billionaire who was the second biggest donor of the 2016 holiday campaign, and veteran hedge fund manager Crispin Odey told Reuters they expect Britain to remain in the EU despite the victory of their electoral campaign the referendum of 2016
Accordingly, Odey, who manages the hedge fund Odey Asset Management, said that he is now positioning for the pound to strengthen after his flagship fund has raised the advantage of betting against UK assets amid wider market concerns about the impact of Brexit.
Britain and the EU reached a hard-won Brexit agreement in November, but the agreement ran aground in the British Parliament. May postponed a vote on the agreement in December to avoid a resounding defeat, and there are few signs that the agreement has picked up support since.
May promised to seek further guarantees from Brussels on the most controversial issue, the status of the Ireland-Northern Ireland Border.
The European Union firmly believes that the legally binding 585-page withdrawal agreement can not be re-opened, but EU officials are looking for of diplomatic formulas that could influence reluctant parliamentarians from the United Kingdom.
The Brexit agreement aims to ensure Britain's smooth departure from the blockade, with a long transition period to adapt to the new situation and negotiate a permanent trade agreement.
Without agreement, Britain faces a sharp rupture from the EU on March 29th and there are fears that it could involve chaotic scenes at borders, ports and airports. Businesses and people in Britain would have to face uncertain weeks and months trying to find out what the unexplored future would bring.
"I do not like the prospect of a 'no deal'. It would be a catastrophe," said Juncker on a visit to Romania, when the nation took over the rotating presidency of the EU.
Many British MPs also oppose the prospect of leaving the EU without an agreement. But many also hate the May agreement, which is unhappy with both sides of the British division of Brexit.
Many parliamentarians who have left the EU say that it leaves the United Kingdom bound by the rules of the bloc and unable to create an independent trade policy, while the pro-Europeans claim it is lower than the friction-free economic relationship that Britain enjoys currently as a member of the EU.
A defeat in Tuesday's vote will leave Britain to set an exit without an agreement 10 weeks later, unless the country's feudal politicians can quickly agree on another plan. Last week, parliamentarians approved an amendment that forced the May government to return to Parliament with a new proposal within three working days of the declined agreement.
But without a majority in Parliament for every single alternating course, there is a growing possibility that Britain may try to postpone the date of departure while the politicians work on a new plan.
Extending the deadline would require EU approval  The official of the EU who spoke on condition of anonymity claimed that this extension was allowed by the government treaty of the EU and that a defeat in Parliament would have put the ball back to Brexit in the British court.
British Foreign Minister Jeremy Hunt warned Friday that the country would face "Brexit paralysis" if parliamentarians refused to agree.
"And the paralysis at Brexit could eventually lead to no Brexit," he told the BBC.