A number of newspapers suggest there are plans to force Mrs May to make way for someone else to take over the helm.
Theresa May's former policy adviser MP George Freeman said it was "all over for the PM", tweeting: "She's done her best. But across the country you can see the anger.
"Everyone feels betrayed. Government's gridlocked. Trust in democracy collapsing. This can't go on. We need a new PM who can reach out (and) build some sort of coalition for a PlanB."
Pro-EU former education secretary Nicky Morgan told the Sunday Telegraph that Cabinet ministers should tell Mrs May "it's time to go", while Brexiteer Steve Baker said potential leadership contenders in the Government should "act now".
But support for the PM has come from Chancellor Philip Hammond.
Speaking on Sky News's Sophy Ridge On Sunday, he said: "This is not about the Prime Minister or any other individual, this is about the future of our country.
"Changing Prime Minister wouldn't help us, changing the party in Government wouldn't help us: we've got to address the question of what type of Brexit is acceptable to Parliament, what type of way forward Parliament can agree on so that we can avoid what would be an economic catastrophe of a no-deal exit and also what would be a very big challenge to confidence in our political system if we didn't exit at all."
Despite a busy public life, Theresa May is a weekly visitor to church.
Speaking to Premier in 2017, she said: "I've been clear and everybody knows that faith plays a part in my life and faith guides me in everything I do."
She also outlined the role her Christian faith plays in her life, saying it is the same today as it was growing up in the vicarage where her father served.
"I continue to practice in the same way that I always have done and I think it's important that one is able to do that," she said.
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