The work and pensions secretary tells Emma Barnett on 5 Live that she "has kept the door slightly ajar".
Staffordshire Conservative MP and Brexiteer Sir Bill Cash asked if the prime minister appreciated the "anger her abject surrender prompted across the country" over her Brexit policy, and whether she would resign.
Theresa May replied: "I think you know the answer to that."
It came after the prime minister told MPs it remains her "priority" to deliver Brexit, defending the decision to delay the UK's exit from the EU by more than six months.
The new deadline of 31 October, set following late-night talks in Brussels, means the UK is likely to have to hold European Parliament elections in May.
Conservative MP Sir Bill Cash attacks Prime Minister Theresa May's "abject surrender" over Brexit.
The UK PM tells MPs about the EU Council summit and sets out plans to resolve the deadlock over Brexit.