Her speech comes after MPs delivered a resounding defeat to May's withdrawal agreement in December, over a key measure created to prevent a hard border in Ireland.
Ms Dorries, a leading Brexiteer warned today: 'A legally binding limit won't pass in Parliament.
Anger has centred on Mrs May's call for fresh negotiations with Brussels over the contentious Irish backstop plan.
"Replacing the current backstop entirely is something all sides could accept".
DUP leader Arlene Foster blasted the PM's plans, commenting that the proposed backstop would create a trade division between Northern Ireland and the UK. However, he will also be seeking assurances that Ireland will not be scapegoated in a no-deal scenario.
Business Secretary Greg Clark was also due to make a statement to parliament on Nissan as Brexit supporters and opponents fiercely debated whether the decision was motivated by Britain's impending withdrawal from the EU. The EU is looking to protect its single market and has said the backstop would only be a temporary arrangement.
But May also admitted that "the need for changes to the backstop is the key issue", with the arrangement now tying the United Kingdom into a customs union with the EU after Brexit in order to prevent a hard border.
"Nor do I have time for those who believe the verdict passed by the British people in 2016 should be overturned before it is even implemented", she added, referring to the rump of MPs calling for a second referendum.More news: Kyrie Irving on future with Celtics - 'Ask me July 1'
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Attorney General Geoffrey Cox last week attempted to originate a "Plan D" Brexit deal in which leading Eurosceptics would form a "joint interpretive instrument" guaranteeing a time-limited backstop.
But the DUP's Emma Little-Pengelly welcomed the Prime Minister's visit and the fact that she would be returning to Brussels "to seek change which can address our objections to the draft withdrawal agreement".
The border has been open since the Good Friday peace agreement of 1998, which largely ended 30 years of conflict in Northern Ireland.
Prime Minister Theresa May has said her commitment to no hard border between Northern Ireland and the Republic of Ireland is "unshakeable" as she prepares for another visit to Brussels to meet European Union leaders.
Speaking about the possibility of a managed no-deal Brexit to an Irish parliamentary committee, Donohoe said that "no such thing exists". Writing in "The Sunday Telegraph", she said she would return to Brussels with a "fresh mandate, new ideas and a renewed determination". He said the government was working with "urgency" on border solutions.
The Withdrawal Agreement had been voted down in the House of Commons last month over the backstop, which could permanently lock Northern Ireland in regulatory alignment with the European Union should London and Brussels not agree a deal on their future relationship by the end of the transition period in December 2020.
"We are absolutely committed to there being no hard border between Northern Ireland and Ireland".
Green Party leader Clare Bailey described Mrs May's speech as "weak and watery words from a weak and wobbly Prime Minister".