Mrs May's hopes of remaining as Conservative leader have appeared doomed since her gamble on a snap election backfired.
Speaking in Japan, Mrs May insisted she was "not a quitter" and would still be Prime Minister at the next election, which is scheduled for 2022. Her invidious predicament recalls that of other embattled Tory leaders past.
"I think it is too early to be talking about going on and on, as Margaret Thatcher once said".
Labour said she was "deluding herself" - but Foreign Secretary Boris Johnson led her defence, insisting she could win an absolute majority.
"Let's get some performance, let's get some delivery for the British people and then let's see where we are, rather than vice versa", Mr Shapps added.
In the event, her fall from power could well mirror Major's - much like Major, May has no parliamentary majority, relies on an informal agreement with the Democratic Unionist Party to stay in power, and leads a party bitterly divided over Europe.
Former cabinet minister Nicky Morgan said it would be "difficult" for Mrs May to lead the party into the next election, while party grandee Lord Heseltine said she did not have a long term future. These are real issues that we need to be dealing with and I'm there to do it.
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On Wednesday, the storm made landfall again, dumping rain on parts of Texas and Louisiana, and leaving a reported 22 people dead. The Grammy victor will be donating all proceeds from the show to Houston relief efforts.
Meanwhile fellow Brexiteer Peter Bone declared: "If she delivers Brexit, and I think she will, then she will be a national hero".
The UK is due to leave the European Union in March 2019 and supporters of Mrs May have said leadership speculation serves only to undermine attempts to secure the best possible terms of exit.
"Yes, that's partly about getting Brexit right, but if you think back to what I said when I became prime minister, when I stood in Downing Street, there are many other issues that we need to address, long-term challenges in our country, ensuring that people don't feel left behind". We know that we have an important and complex job to do and Theresa May deserves our support as she sets about that.' Similarly Charles Walker, the vice chair of the powerful group of backbenchers, says: 'Good for her, to be honest.
As well as her trade mission, Mrs May has supported the nation's efforts against North Korea. "Frankly, she is a disaster", said the anonymous Tory.
Most Britons think the Conservative Party will be worse off if Theresa May remains as leader, an exclusive Sky Data poll reveals.
Most scathing of all was George Osborne, the former MP and Chancellor under David Cameron turned newspaper editor.
The idea that she now wants to spend another five years as party boss came as a surprise to some of her MPs.
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