Brexit minister David Davis was reportedly furious and considered quitting over May's plan in which Britain could stay aligned to the EU's customs union for years after leaving the bloc.
May held separate face-to-face meetings on Thursday morning with Davis and fellow eurosceptics Boris Johnson, the foreign secretary, and trade minister Liam Fox, her Downing Street office said.
Asked if she expected Davis to remain in his position at the end of the day, the prime minister's spokeswoman said: "Yes... of course."
The so-called backstop proposal would kick in only if no other solution were found to avoid customs checks between Northern Ireland and EU member Ireland, but there are fears if implemented that it would last indefinitely.
Davis was said to be concerned about the lack of an end date, and was pushing for a provision stating that Britain can withdraw unilaterally from the arrangement -- something Brussels is unlikely to accept.
May's meetings with her ministers came just hours before the cabinet sub-committee charged with taking key decisions on Brexit was due to meet at lunchtime.
Downing Street sources initially said the committee was not going to talk about the backstop, implying it was already agreed in principle.
However, Davis told reporters on Wednesday that it would, saying: "It would be improper of me to pre-empt the negotiation there, but I suspect it will be fairly decisive tomorrow."
Asked if he could stay in his job if the proposals did not have his explicit approval, he said: "That's a question I think for the prime minister to be honest."
Sarah O'Grady, a newspaper journalist and the wife of Davis's chief of staff, had tweeted early Thursday: "Backstop not backed up by DD. Crunch time."
The government insists that it has no intention of using the backstop, and will instead find a way to avoid border checks in Ireland through an overarching trade deal with the EU.
However, striking a new trade deal could take years.
The latest round of Brexit negotiations wrap on Friday, but hopes of a breakthrough at the next EU summit in Brussels at the end of this month are fading.
Both sides say they want to agree a deal by October, to allow time for it to be ratified before Brexit on March 29, 2019.