"If we were not to vote for that, I'm not sure I would give it much more than 50-50", he told The Sunday Times.
The parliamentary vote is scheduled for the week of January 14, with many members of parliament still fiercely opposing the so-called backstop arrangement aimed at preventing a post-Brexit hard border on the island of Ireland. The Brexit deal I have negotiated delivers on the vote of the British people.
Downing Street has said there is "still work to do" - as the PM seeks to persuade sceptical Conservative MPs, some of whom believe the agreement does not represent the Brexit the country voted for in 2016.
"So the British will be able to perform from the very first day of checks, and so we will make it", said Malmström.
The Defense Secretary proposes that Britons should be more hopeful about the post-Brexit future of the UK.
DUP leader Arlene Foster used her New Year message to warn Mrs May she will need to make significant changes to her Withdrawal Agreement if the Northern Irish party are to back it. We just want clarity on the future relations.
"When we have the vote, members will need to reflect carefully on what is in the best interests of our country", she said, stressing that she had won significant assurances from European Union leaders over the contentious Irish "backstop". "If parliament backs a deal, Britain can turn a corner". It had been scheduled for December, but the prime minister postponed it at the last minute, amid near-unanimous expectations that she would lose heavily.
Her chances of success could also depend on persuading some Labour MPs that the only alternative to her proposals is a disorderly no-deal departure from the EU.
"You can see the frustration in members of parliament trying to navigate what the people wanted when they voted on the referendum", he said.
The Brexit uncertainty found echoes in Liberal Democrat leader Vince Cable's speech as well, who said a second referendum was "the only way forward".
Separately, the Times reported that exiting the European Union without a deal would trigger a cut in taxes and interest rates and the return of quantitative easing, according to the newspaper's annual survey of economists.
"They realize that we are good partners and actually the values that we stand for, of tolerance, democracy and justice, these are the values that they hold dear to their hearts", said Williamson.