The legal advice confirmed that Britain can't unilaterally opt out of the backstop, which requires an agreement by both sides.
She said those backing a second referendum wanted the public to give a different message.
Overwhelmingly, the message I've heard is that people want us to get on with it.
"We do this by removing each option in turn, and then looking at the second choice of people who backed that option".
"I think Parliament has been given its instructions by the people of the United Kingdom as a whole to get on with Brexit".
During Prime Minister's Questions, East Londonderry MP Gregory Campbell accused the prime minister of allowing the Irish border to become a "negotiating ploy" by the European Union, adding that the backstop was based on a "false political assertion".
If parliament rejects her deal, Mrs May has warned Britain could leave without a deal or that there could be no Brexit at all.
May's chances of survival were dealt a blow on Tuesday when her government suffered a humbling hat-trick of defeats in the Commons over Brexit legal advice.
Sir Chris, a staunch Brexiteer, is opposed to the Prime Minister's deal.
Ministers are expected to set out today how this will be done.
Meanwhile, British MPs entered the second day of a five-day marathon debate over the agreement signed with the European Union, which needs to be ratified by Parliament with a majority for it to go through to the next stage in time for Britain's formal exit from the European Union on March 29, 2019.
Before the prime minister appeared at the despatch box, her government had gone down to defeat for the third time in an hour.More news: Arrest in Australian cold case made famous by podcast
In his advice, dated 13 November, Mr Cox says signing up to the backstop was a "political decision".
Last month the Prime Minister delivered a stark ultimatum to MPs - her deal, no deal or no Brexit.
After a complaint presented by a group of cross-party lawmakers, parliamentary speaker John Bercow said he believed it could be argued that a contempt had been committed because of the failure to release the full legal advice.
Britain's Finance Minister Philip Hammond concurred, saying it is a delusion to think that the government will be able to negotiate a new divorce deal if May's agreement is defeated in a vote in Parliament next week.
"The prime minister can't keep pushing Parliament away or avoiding responsible scrutiny".
Failure in the vote will transform the quarterly European Union summit to be held in Brussels next Thursday and Friday into a "Brexit crisis" meeting, officials say - though the timing may mean it is too soon for May to tell fellow leaders much more than that she has failed at her first attempt and needs more time.
"The fact is, during the course of this administration we have won the overwhelming majority of votes that have taken place on the floor of the House of Commons".
During the first two days of debate, at least 15 of May's own lawmakers explicitly said they intend to vote against the deal, and British media have speculated that as many as 100 could ultimately rebel.
He placed a 10% probability on a no-deal Brexit, down from 20%, and a 50% probability on an orderly Brexit, down from 60%.
She said: "I am talking to colleagues about how we can look at parliament having a role in going into that and coming out of that".
Mrs May told them: "I promise you today this is the very best deal for the British people, I ask you to back it in the best interests of our constituents and our country".