Baroness Warsi, the senior Minister of State at the Foreign Office, raised eyebrows at Westminster when she declared that the Home Secretary had been doing "a fantastic job" and added that both she and Mrs May fully supported Mr Cameron, noting: "Theresa, like me, would agree that we have full confidence in the Prime Minister."
When the UK Government is under fire, it is usually the PM who has to make clear that he has full confidence in his ministers – not the other way round.
The latest poll placed the Tories on just 27%, one of its lowest ratings in recent years. UKIP is just 10 points behind on 17% after luring voters away from the Tories and Labour, most recently at the Eastleigh by-election.
It also found Mr Cameron's personal rating had dropped 8% in a fortnight to just 18%.
It follows a poll of marginal constituencies that suggested Labour would scoop 93 seats from the Conservatives and win the next General Election..
Today, Liam Fox, the former Defence Secretary, will say that the Coalition's cut in the welfare budget should be matched by tax cuts, which leave more money in people's pockets to stimulate the economy.
Dr Fox will argue that structural taxes are inhibiting growth and will say: "I would like to see Capital Gains reduced, if possible to zero, for a defined period before being reintroduced at a more sensible level.
Earlier, Mrs May laid out her leadership ambitions by saying the next Tory government would scrap the Human Rights Act and "consider very carefully" Britain's relationship with the European Convention on Human Rights, as well as aim for "even more radical" reform of public services.