Theresa May has asked MPs to make an “honourable compromise” as she seeks to persuade them to back her Brexit deal at the third time of asking.
Writing in the Sunday Telegraph, the prime minister said failure to support the deal would mean “we will not leave the EU for many months, if ever”.
Mrs May is expected to bring her withdrawal agreement back to the Commons next week for a third vote.
It comes after MPs this week rejected her deal and voted to delay Brexit.
Former Cabinet minister Esther McVey, who resigned over the Brexit agreement, told Sky’s Sophie Ridge programme that she would “hold my nose” and vote for the deal after rejecting it twice herself, as it was now a choice between “this deal or no Brexit”.
And a letter signed by 15 Tory MPs from Leave-backing constituencies, including former Brexit Secretary David Davis, also urged colleagues to back the deal.
But International Trade Secretary Liam Fox warned the vote could be pulled, telling Sophie Ridge it was “difficult to justify having a vote if we knew we were going to lose it”.
The EU will decide the terms and conditions of any extension. Legally, the UK is still due to leave the EU on 29 March.
Meanwhile, Labour leader Jeremy Corbyn has written to MPs across the Commons inviting them for talks to find a cross-party compromise.
He also told Sky that while he “has to see the wording of it”, Labour MPs would be told to vote in favour of an amendment calling for another referendum next week, and he said he may propose another vote of no confidence in the government if the PM’s deal is voted down again.
Mrs May says if Parliament votes for her withdrawal deal before an EU leaders’ summit on Thursday, the UK will seek a short delay to Brexit to pass the necessary legislation.
“That is not an ideal outcome – we could and should have been leaving the EU on 29 March,” she said.
“But it is something the British people would accept if it led swiftly to delivering Brexit. The alternative if Parliament cannot agree the deal by that time is much worse.”
If a deal is not agreed before Thursday, EU leaders are contemplating a much longer delay.
Mrs May said it would be a “potent symbol of Parliament’s collective political failure” if a delay to Brexit meant the UK was forced to take part in May’s European elections – almost three years after voting to leave the EU.