Meanwhile, Britain's Parliament narrowly approved financial roadblocks that are created to make it more hard for the country to leave the European Union without a Brexit deal, giving a defeat to Prime Minister Theresa May's government.
The amendment was tabled by Labour MP Yvette Cooper and former Tory cabinet minister Nicky Morgan in an effort to demonstrate the strength of opposition to no deal.
Her proposal aims to restrict the government's freedom to use the Finance Bill to make tax changes linked to a no deal Brexit without the "explicit consent" of Parliament.
Prime Minister Theresa May is trying to force her Brexit deal through parliament but lawmakers are expected to reject it.
The PM looks set to confirm what David Lidington, her de facto deputy, said during a Holyrood visit in November that Great Britain would "not diverge from the regime" of European Union regulations, which Northern Ireland would abide by during the backstop; thus, there would be no border down the Irish Sea. "That is why we are taking every opportunity possible in parliament to prevent no deal".
"Theresa May must now rule out no deal once and for all".
She later announced the vote would go forward in the week beginning January 14.
It is not an absolute block to leaving the European Union without a deal because it does not negate the legislation already in place stating that Britain will leave the European Union on March 29.
Asked whether he was prepared to resign to stop a no-deal Brexit, he replied: "Definitely, I would".
That support could drop to 26 percent - lower than Labour has scored at any general election in the past century - if Labour MPs help Theresa May's deal through Parliament. The withdrawal agreement is good both for the United Kingdom and for the EU.More news: Transformer explosion at power plant turns New York skyline blue, causes outages
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She consulted with European leaders in the days that followed, but it wasn't clear she gained any new commitments from them.
Mr Jenrick said clause 89, which was the subject of the amendment, ensured no more than "the most minor and technical changes", adding: "Clause 89 is simply prudent preparation to provide our taxpayers with the certainty they deserve".
Meanwhile, Business Secretary Greg Clark told the House of Commons that a no-deal Brexit "should not be contemplated". "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", the spokesman said.
The prime minister was forced to abandon plans to hold a vote on the deal in December after more than a hundred Conservative MPs and the Democratic Unionist Party, which props up May's minority government, vowed to vote against it.
Some Brexit supporters say a no-deal exit is the only way to truly leave the bloc and that warnings of the economic consequences have been overblown to drum up support for May's plan.
More than 100 Tories vowed to join with Labour to defeat May's deal, prompting her to go back to Brussels to get guarantees the backstop would only ever be a temporary measure.
"There are no negotiations, because all we have on the table is what we consider given, acquired and approved", he said.
He said support for leaving without a deal was "hardening".
It has been suggested that Brexit could be delayed if the deal is defeated in the "meaningful vote" to allow time to renegotiate elements of the deal.
"If the deal is not voted on at this vote that's coming up, then actually we're going to be in uncharted territory", May said on the BBC's Andrew Marr Show.