People aged 35-54 think she does more bad than good for the Conservatives by 41% to 29%, while people aged 55 and over are equally split, with 37% saying she is good for the party, 36% bad. There's a real job to be done in the United Kingdom.
One MP has told the FT that the prime minister appears to be "harbouring delusions" and that she can not win a general election.
The prime minister has sought to consolidate her position by negotiating a governing agreement with the Democratic Unionists and overhauling the way Downing Street works, replacing key advisers.
The next general election is not scheduled to take place until May 2022, by which point Mrs May - if she stayed in Downing Street - would have been prime minister for almost six years.
Asked on the first day of her trip to Japan by both the BBC and ITV if she meant to lead the ruling Conservative party into the next election, pencilled in for 2022, she replied "Yes" before underlining her determination to continue.
Grant Shapps, a former Conservative Party chairman, was among MPs to air the party's disquiet over May's leadership, even comparing her to Margaret Thatcher. "I'm in this for the long term".
He said: "We'll end up having to pay more".
"The best scenario for us is that Britain cancels its Brexit decision", said Ichiro Hara, head of the global affairs bureau at Japan's top business lobby Keidanren.
Labour's Jon Trickett added: "The Prime Minister is deluding herself".
But her Foreign Secretary Boris Johnson who has long touted as a potential successor to Mrs May, threw his support behind the Prime Minister. She really wants to deliver it.
One unnamed Tory former minister said Mrs May may have ended up "hastening her own demise", while a senior MP said they were "utterly dismayed" by the remarks. I would like nothing more for Theresa May, if she can not find the affection of the British public, to find admiration and respect.
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.
Japan's top government spokesman Yoshihide Suga said her attendance at the meeting underscored the two countries' close ties, after May this week said she was "outraged" by Pyongyang's provocative missile launch.