The American they will face Australia and Serbia on July 15 and July 17 as part of their preparation for the Paris Olympic Games
The prime minister has already pulled the vote once with defeat looming, and a loss for the government would plunge Britain into "uncharted territory", according to May, putting the whole process up for grabs.
May is still seeking assurances from the EU on the most controversial elements of the Brexit deal relating to Northern Ireland, in a bid to convince critics to back the agreement.
These assurances are set to be delivered to lawmakers before they vote, although not before they start their debate on Wednesday.
"The work to secure those assurances is ongoing. I think what's important is that if we are to secure assurances, MPs are aware of what they are before the vote takes place," a Downing Street spokesman said.
The government has recently made much-publicised preparations for leaving without a deal, with Britain legally due to leave the EU on March 29, regardless of whether May's deal is approved.
MPs want to intervene to prevent this from happening, and they narrowly voted on Tuesday for an amendment that would curtail the government's tax powers in the event of no deal.
"The amendment doesn't affect the normal operations of the Treasury... but it does make it harder for the government to drift into no deal without parliament being able to direct it," Yvette Cooper, the MP who introduced the amendment, told the Guardian.
Other MPs would be in favour of a second referendum but such a move would likely cause outrage among Brexit voters and raise the issue of the framing of the question.
A PR battle has reached fever pitch as the deadline looms, with second referendum campaigners setting up stalls at markets nationwide, while Brexiteers are also touring the country pushing for a clean break.
May insists Britain will leave the EU in March whatever happens, but there is growing talk of delaying the two-year Article 50 exit process to give her some breathing space to get her deal agreed.
An EU diplomat told AFP on Tuesday that "we are convinced that Theresa May will request a postponement after the agreement is rejected in the British parliament."
Sources in Brussels have told AFP for several weeks that Britain has been discussing the possibility with European officials, while this was also reported in the Daily Telegraph newspaper on Tuesday.
Brexit Secretary Stephen Barclay denied the reports, saying "there are people in the European Union who are discussing this issue, but that is not the position of the UK government."
The prime minister survived a half-hearted attempt by her party to oust her before Christmas, but the level of rebellion has left her weakened.
The key sticking point is the deal's so-called backstop solution, which proposes some kind of customs union to prevent a hard border between the British province of Northern Ireland and the Republic of Ireland.
Brexit supporters are worried that there is no mechanism for Britain to unilaterally withdraw, meaning it could end up indefinitely stuck in the union, hampering its ability to strike deals with the rest of the world.
Irish leader Leo Varadkar reportedly said Tuesday that the EU is "happy to give" fresh assurances over the backstop.
"We don't want to trap the UK into anything," he told the Irish Times.
The American they will face Australia and Serbia on July 15 and July 17 as part of their preparation for the Paris Olympic Games
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