She seems to be headed for deadlock as prominent Brexiteers within her team have rubbished her proposal of a so-called "customs partnership", under which the UK would collect tariffs on behalf the EU after it has left the union.
A second proposal centres around a more technology-driven system of minimum customs checks dubbed "maximum facilitation" which is favoured by some members of the Cabinet over the other.
But there appears to be no consensus in sight for the British prime minister to progress on the issue.
You can trust me to deliver. The path I am setting out is the path to deliver the Brexit people voted for. I will not let you down, she writes in 'The Sunday Times'.
Of course, the details are incredibly complex and, as in any negotiation, there will have to be compromises. But if we stick to the task we will seize this once in a generation opportunity to build a stronger, fairer Britain that is respected around the world and confident and united at home, she adds.
Her intervention came after tensions in the Cabinet emerged into the public domain last week as UK foreign secretary Boris Johnson, a staunch Brexiteer, launched an attack on May's preferred option for a post-Brexit EU customs partnership.
He dismissed the proposal as "crazy", saying it would deny Britain control over its trade policy.
"Because it is novel, because no model like this exists, there have to be significant question marks over the deliverability of it on time," Gove said.
"More than that, what it requires the British government to do is, in effect, act as the tax collector... for the European Union...It is my view that the new customs partnership has flaws and that they need to be tested," he added.
Keir Starmer, from the Opposition Labour party which favours remaining within a customs union with the EU post-Brexit, said as neither of the options were "workable nor acceptable to the EU" and, with time running out, UK Parliament must force the government's hand by backing a "comprehensive" customs union.
May has insisted that the final Brexit deal must honour the agreements in the Northern Ireland peace process and not create any hard border between Northern Ireland and the rest of the UK, creating the prospect of impasse over the issue.
Simon Coveney, the Irish foreign minister, dismissed the idea of using any form of infrastructure or technology to maintain separate customs regimes between the Republic of Ireland, an EU member, and Northern Ireland, which will become a non-EU member after Brexit.
Meanwhile, a cross-party group of former Cabinet ministers including former Liberal Democrat leader Nick Clegg and former Labour foreign secretary David Miliband are trying to build pressure on the British Parliament to vote to remain in both the customs union and the single market after Brexit, arguing it is vital for the economy.
Student organisations representing almost a million young people have also written to MPs demanding a referendum on any final Brexit deal.
(This story has not been edited by Business Standard staff and is auto-generated from a syndicated feed.)