Time is running out for Mrs May to secure a withdrawal agreement with the EU before Britain officially leaves the bloc on March 29 next year.
Your government must still agree on a consensus for Britain's future relationship with the EU more than two years after the historic referendum in June 2016.
His party is deeply divided along the Brexit lines, with Staying and leaving the deputies threatening to overthrow his government if he takes the Brexit down a path unpleasant to his.
Now, a major YouGov poll suggests that the events of the last two years have changed public opinion on the issue of leaving the EU.
The survey of 10,000 adults found that Remain would win a second referendum between 53% and 47%, a reversal of the result in 2016, when Leave won with 51.9% of the vote.
On the question of the final agreement, 45% think that a public vote should be held, while 34% oppose, according to the survey, one of the largest since the referendum in 2016.
Activists and pro-EU politicians said the YouGov study, commissioned by the Popular Vote lobby, showed that people are changing their minds about Brexit.
Peter Kellner, a leading pollster and former YouGov president, said the findings were "politically significant."
He said: "Across the spectrum, the message of the voters in this survey is clear: if the government and the parliament can not resolve Brexit, the people should."
"If the government and parliament can not solve Brexit, people should"
Surveyor Peter Kellner
Labor voters overwhelmingly said they would stay in the EU again, between 77% and 23% for Leave.
The majority supports a referendum on the exit agreement, 63% compared to 18%.
Kellner said polls showed the chasm between Labor members and leaders for their approach to Brexit.
"Labor supporters overwhelmingly support a new public vote and, in resisting this, party leadership is increasingly alienated from its own voters," he said.
"If these findings emerged from a conventional survey of 1,000-2,000 respondents, the findings related to the subsamples should be considered with caution.
"But this exceptionally large survey of 10,000 shows contains more than 2,700 current Labor supporters, leaving no doubt about the size of most of them for a new public vote."
Labor MP Chuka Umunna, who supports the Popular Vote campaign, said the results of the YouGov poll show that there has been a change in opinion about Brexit.
He said: "Politicians everywhere are increasingly caught within the red lines of their own creation, but the impulse this summer is with the campaign for the popular vote as more and more people realize that it is the only way to regain control of the process.
"It is clear from YouGov's findings that public opinion is moving behind the popular vote across the political spectrum."
People took the streets of London to march for a second EU referendum
He called Labor leader Jeremy Corbyn to differentiate the party's position on the Brexit government by backing a Popular Vote on the final agreement.
"This survey shows that Labor voters overwhelmingly support the popular vote, putting them at odds with the party's pro-Brexit official position.
"The Labor Party must now do what its members, its supporters and voters are crying out for: to put a clear kill-pot between the opposition and the government, and to provide leadership to the country by supporting the Popular Vote campaign."
The 10,121 adults who participated in the survey were surveyed between July 31 and August 7.
The figures have been weighted and are representative of all GB adults.