While Brexit Secretary Steve Barclay said there had been "some movement" from MPs to support the agreement which is widely expected to be defeated, he said he thought that if it fell the Commons would eventually support something "along the lines of this deal".
British Prime Minister Theresa May said on Sunday that a failure to support her Brexit deal will be catastrophic for Britain.
Failure to deliver Brexit would be "incredibly damaging" for democracy and something the United Kingdom would regret for "many, many generations", he said.
He appealed to MPs who have spent months fighting for their "number one top favourite outcome" to come together behind a Withdrawal Agreement which is "not perfect" but "broadly delivers Brexit".
But he opened the door to the vote taking place before the end of the week as he said: "It is going to be soon, don't worry about that".
"I don't like the prospect of a no-deal".
He said people should "see what happens" following Tuesday's critical vote.
He said if it is defeated, Britain should continue to press the European Union for a deal that "respects the referendum but if Brussels' "intransigence" persists "we must be willing to leave the European Union at the end of March on World Trade Organisation terms".
While a large majority of party members, according to polling, want Corbyn to actively seek a new referendum, the Labour leader has previously said it is more likely he would push to take the United Kingdom out of Europe with a different deal.
Elsewhere, it emerged that Speaker John Bercow met Tory remain rebel Dominic Grieve on Tuesday, the day before his controversial decision to allow MPs a vote on Mr Grieve's amendment to the timetable of the Brexit deal. "We ignore that and the will of the people at our peril".
In a significant shift of tone apparently created to win over hardline Brexiteers who have set their faces against Mrs May's deal, Mr Hunt warned that defeat next week would not necessarily provide MPs with the opportunity to choose their preferred version of Brexit.
Mr Grayling said there would be a "different tone" in British politics if the United Kingdom failed to leave the European Union, and predicted a "less tolerant society" and a "more nationalistic nation".
Northern Ireland Secretary Karen Bradley said a no-deal exit would create a "feeling of unrest". The vote was postponed at short notice in December after the Prime Minister faced a humiliating defeat by politicians.
"This is too important for political game-playing and I urge Conservative MPs who back Brexit and others to back the deal. I just can't see how it happens with that configuration of Parliament".