Theresa May is set to hold a series of private meetings with backbench MPs as she bids to win support for her Brexit deal before Tuesday’s historic vote.
The withdrawal agreement has been endorsed by EU leaders but now needs Parliament’s backing.
Newspaper reports over the weekend said the vote would be delayed – but Number 10 insists it will go ahead as planned.
The PM said a rejection of her deal could lead to a general election – or possibly “no Brexit” at all.
The government is widely expected to lose the vote, with Labour, the Liberal Democrats, the DUP, the SNP and dozens of Conservative MPs saying they cannot support the deal.
Downing Street believes most Conservative MPs could support Mrs May’s deal if it were not for the backstop – the insurance policy designed to prevent a hard border in Ireland.
On Sunday evening, Mrs May spoke on the phone to Irish Prime Minister Leo Varadkar, whose support could be vital if she were to negotiate further with the EU.
She also spoke to the European Council President Donald Tusk, who tweeted it would be “an important week for the fate of Brexit”.
Boris Johnson said Mrs May could stay on if she lost Tuesday’s vote – but must renegotiate the deal with Brussels.
Mr Johnson, who quit the cabinet over Mrs May’s Brexit strategy, told the BBC he did not want a “no-deal” Brexit or another referendum, but it was not right to say there were no alternatives.
He said the Northern Ireland “backstop” put the UK in a “diabolical negotiating position”.
MPs could give Mrs May “a powerful mandate to change that backstop” by voting it down on Tuesday, he said.
Meanwhile, Lib Dem leader Sir Vince Cable believes Brexit may not happen at all.
“Increasingly I doubt it,” he said when asked about it becoming a reality, adding it was “more likely that it won’t happen”.
He added there could be a “hell of a backlash” if Mrs May’s “economically damaging” Brexit was imposed without another referendum.
Monday morning will also see the European Court of Justice (ECJ) rule on whether or not the UK can cancel Brexit without the permission of the other 27 EU members.
Anti-Brexit politicians and campaigners have argued the UK should be able to unilaterally halt the Brexit process if it wants to do so.
Their case has been opposed by the UK government and the EU itself. But a senior ECJ official said last week he agreed the UK should be able to change its mind about leaving.
The court will now deliver its final decision in the case, with the ruling expected to be published at about 08:00 GMT.