The Prime Minister has continually said her terms represent a "good deal" and that no-deal exit is not her preferred outcome.
Conservative MPs Sir Oliver Letwin, Sarah Wollaston, and Nick Boles along with Labour chairman for the Brexit select committee Hilary Benn have backed the changes.
During his speech in the Commons, Letwin sounded nearly tearful as he said he would rebel against the Tory whip.
Theresa May has said repeatedly that her Government has no plans to extend Article 50.
"Less than a hundred lorries is a drop in the ocean compared to the more than 10,000 that go to the channel ports every day", said Charlie Elphicke, a Conservative lawmaker for Dover. "The prime minister knows everybody's views and I think my view is not an uncommon one".
May did not respond to an urgent question tabled by Labour leader Jeremy Corbyn "on progress made in achieving legal changes to the European Union withdrawal agreement and the timetable in this House for the meaningful vote", but is due to face him during Prime Minister's Question Time on Wednesday.
Analysts said May's comments to the BBC did little to hide the fact the British leader has no "gamechanger" amendments to the proposed withdrawal agreement capable of swinging the parliamentary arithmetic in her favour.
Lawmakers are also taking legislative action to try to prevent "no deal".
Cooper explained in a piece for The Guardian today: "The amendment doesn't affect the normal operations of the Treasury and government".
Brexit will take effect March 29.
Labor says it would renegotiate the deal, and is angling for new elections. "The government has got us to the point of ruin".
"Everyone recognizes that Brexit is an existential threat to the United Kingdom automotive industry and we hope a practical solution will prevail", he said, calling for lawmakers to support May's deal to guarantee a transition period. But May would be long gone before March if she fails to deliver on her promises.
"It would be a gross dereliction of responsibility of members of this house to inflict a no-deal situation on our constituents", she said.
The test at the disused airfield comes as no-deal preparations are ramped up amid bitter deadlock over Brexit in Parliament.
"I want us to proceed with Brexit, I want to find the will of the House".
Debate will resume on Wednesday and the vote is officially slated for the week of January 14, but MPs look no closer to reaching agreement.
Cooper told the Commons MPs had a responsibility to act.
Liam Fox, the global trade secretary, called the amendment "irresponsible" as it would tie the hands of the government. However, the amendment does not block no deal in itself; instead it simply makes that option more hard to navigate.
Downing Street described it as an "inconvenience" which would not prevent the Government collecting taxes. A UK Government spokesman said it will work with parliament to ensure the tax system works smoothly in all Brexit scenarios.