May's Northern Irish supporters vehemently oppose any checks between the province and mainland Britain after Brexit.
The head of the Democratic Unionist Party, Arlene Foster, said May "could not in good conscience" back an EU proposal for checks on goods being imported to Northern Ireland from Britain after Brexit.
Under May's proposals, the whole of the United Kingdom would forge a customs partnership with the EU after a transition period ends in December 2020 in the event of the backstop being triggered.
Some of May's ministers have urged her to put a time limit on that plan.
The Times newspaper said May was warned the issue was so serious that she could face further cabinet resignations unless she found a way to ensure the backstop was not permanent.
Speaking to Northern Ireland journalists at her Downing Street office, May said on Thursday that talks on the Irish backstop were likely to continue until November.
