Since her botched bet on a snap election in June 2017 lost her party its majority in parliament, May has faced persistent talk of a leadership challenge which has weakened her as she tries to clinch a Brexit deal with the European Union.
Lawmakers from the European Research Group (ERG), a grouping in May's Conservative Party which wants a sharper break with the EU, met on Tuesday night and openly discussed May's future. Unattributed comments included "everyone I know says she has to go", "she's a disaster" and "this can't go on," according to BBC.
One source quoted by BBC said "people feel the leadership is out of touch and has lost the plot" but another said changing the leader "is a stupid idea now".
A spokesman for May declined to comment on the report.
Publicly, the leading party skeptics pledged their loyalty.
When asked if May should go, Jacob Rees-Mogg, the ERG leader, told reporters: "The policy needs to be changed but I am supporting the person. Theresa May has enormous virtues, she is a fantastically dutiful prime minister and she has my support – I just want her to change one item of policy."
Former Brexit secretary David Davis, who quit the cabinet in July over May's EU withdrawal plan, said: "I disagree with her on one issue -- and it's this issue -- and she should stay in place because we need stability and we need decent government."
The pound fell against the dollar to as low as $1.2994 but later recovered to trade flat at $1.3028.
The United Kingdom is due to leave the European Union on March 29. The EU and Britain hope to clinch a deal later this year so parliaments on both sides can ratify it before Brexit.
European Commission head Jean-Claude Juncker said the EU will not allow Britain to participate only in some parts of the bloc's single market after Brexit without honoring all of the rules.
May's proposal for a post-Brexit free trade area with the EU for goods, which would include accepting a "common rulebook" for those goods, have angered committed Brexiteers inside her party.
Even a small rebellion inside her party on a final deal could spell the end of her minority government and throw Britain's exit into chaos.