The next days will be crucial to know if an agreement is reached at the Brussels summit on Thursday.
United Kingdom Prime Minister Boris Johnson is approaching key parliamentary figures needed to approve a Brexit agreement while euro sceptics and pro-treatment Labour indicate that they could support a new agreement with the European Union.
The premier will have to win over most of the conservatives votes who opposed Theresa May, as well as the Democratic Unionist party or some of the Labour MPs if he manages to bring an agreement from Brussels.
There are indications that the Euro sceptics are now supporting the agreement, partly because they fear that Labour might try to push for a second referendum instead of an election.
Lee Rowley, a Conservative MEP who voted against May's agreement on three occasions, gave a speech saying that he had changed his position and that his opinion now was that the parliament should do Brexit.
"We are in a difficult situation and in the last few days, at least there is hope that this toxic and paralyzing fog, which we have created, may be disappearing as the Prime Minister outlines a way forward," he said, adding that "this is a moment of decision and we were chosen to make decisions."
Another Tory who voted against the May agreement told the Guardian "whatever the Prime Minister brings, I'm going to take a very long and pragmatic look at it because I think a second referendum would be a disaster."
Some 18 Labour MEPs signed a letter last week urging the EU to work day and night to reach an agreement.
The next few days will be crucial to know if an agreement is reached at the European summit on Thursday.
The government will have to table a motion in Parliament by Wednesday if it wants to call MPs to a Saturday session to discuss any agreement. Yet if a deal can be agreed, it will be rushed through Parliament before the Oct. 31 deadline, with both the House of Commons and the House of Lords sitting through the night.
The British parliament has rejected three times the withdrawal deal agreed between the last government and the EU, deepening a three-year crisis that threatens Britain's status as one of the world's pre-eminent financial centers and a stable destination for foreign investors.